Day 3 examples a
•
0 likes•176 views
This document discusses stretching and compressing functions both horizontally and vertically. It provides examples of compressing functions vertically by factors like 1/3 and horizontally by factors like 1/2 or -2 which compresses the graph left or right respectively. Functions can be stretched or compressed by applying factors to the input or output values.
Report
Share
Report
Share
Download to read offline
Recommended
Perp hints
Two lines are perpendicular if their slopes have a product of -1. The slopes of perpendicular lines will always satisfy the property of having a product of -1.
Utility maximisation and regret minimisation - a mixture of a generalisation
Utility maximisation and regret minimisation - a mixture of a generalisationInstitute for Transport Studies (ITS)
Poster presented at TRB 2015.
www.trb.org/AnnualMeeting2015/annualmeeting2015.aspx
www.its.leeds.ac.uk/people/s.hessGreat Pyramid of Giza and Golden Section Transform Preview
The document discusses connections between the Great Pyramid of Giza and the Reverse Order Low Golden Section Transform (RLGST). It provides code examples for performing the 2D RLGST and its inverse on an image. The RLGST is based on the golden ratio, Fibonacci numbers, and the Wythoff sequence. There may be mathematical relationships between the dimensions of the Great Pyramid and properties of the RLGST that could reveal insights into ancient engineering. References are provided on the RLGST, wavelets, Fibonacci words, and the Great Pyramid.
2a. Introduction to Calculus (change)
This document discusses rates of change and differentiation. It explains that differentiation finds the rate of change of a function, while integration finds the total change. Specifically, it shows that differentiation involves multiplying a function by its power and reducing the power by 1, while integration involves raising the power by 1 and dividing by the new power. Examples are provided to demonstrate finding the gradient and rate of change of linear, quadratic, and other polynomial functions using differentiation, as well as using integration to find total change over an area under a curve.
Image Compression Comparison Using Golden Section Transform, Haar Wavelet Tra...
Image Compression Comparison Using Golden Section Transform, Haar Wavelet Transform and Daubechies D4 Wavelet By Matlab
Gradient of graph
The gradient of a line measures how steep the line is, and can be positive, negative, or zero. The gradient is calculated by taking the change in y over the change in x between two points on the line. If the line is vertical, its gradient cannot be determined. Examples are provided to demonstrate calculating the gradient using points on a line and the formula for change in y over change in x.
Learning objects lo4
- Sound waves are longitudinal waves that propagate in three dimensions through pressure variations caused by particle displacements.
- The speed of sound can be calculated using the bulk modulus and density of the medium using the equation v=√B/ρ.
- The mathematical description of the displacement amplitude of a sound wave is s(x,t)=smcos(kx-ωt+φ), where sm is the maximum displacement, k is the wave number, ω is the angular frequency, and φ is the phase constant.
- The relationships between displacement, pressure, and intensity can be determined from the equations Δp(pressurechange)=Bk smsin(kx-ωt+φ) and I=1/2
Cluster abundances and clustering Can theory step up to precision cosmology?
This document discusses improvements to the Press-Schechter theory for modeling the abundances and clustering of dark matter halos. It proposes that modeling halo collapse as requiring the density to "step up" above a critical density threshold at progressively larger spatial scales provides a better approximation than assuming fully correlated or uncorrelated densities. This "stepping up" approach requires only 2-point statistics and can be applied to non-Gaussian fields. The document also suggests that modeling the distribution of density slopes at peak positions provides a way to match halo counts through an Excursion Set Peaks model.
Recommended
Perp hints
Two lines are perpendicular if their slopes have a product of -1. The slopes of perpendicular lines will always satisfy the property of having a product of -1.
Utility maximisation and regret minimisation - a mixture of a generalisation
Utility maximisation and regret minimisation - a mixture of a generalisationInstitute for Transport Studies (ITS)
Poster presented at TRB 2015.
www.trb.org/AnnualMeeting2015/annualmeeting2015.aspx
www.its.leeds.ac.uk/people/s.hessGreat Pyramid of Giza and Golden Section Transform Preview
The document discusses connections between the Great Pyramid of Giza and the Reverse Order Low Golden Section Transform (RLGST). It provides code examples for performing the 2D RLGST and its inverse on an image. The RLGST is based on the golden ratio, Fibonacci numbers, and the Wythoff sequence. There may be mathematical relationships between the dimensions of the Great Pyramid and properties of the RLGST that could reveal insights into ancient engineering. References are provided on the RLGST, wavelets, Fibonacci words, and the Great Pyramid.
2a. Introduction to Calculus (change)
This document discusses rates of change and differentiation. It explains that differentiation finds the rate of change of a function, while integration finds the total change. Specifically, it shows that differentiation involves multiplying a function by its power and reducing the power by 1, while integration involves raising the power by 1 and dividing by the new power. Examples are provided to demonstrate finding the gradient and rate of change of linear, quadratic, and other polynomial functions using differentiation, as well as using integration to find total change over an area under a curve.
Image Compression Comparison Using Golden Section Transform, Haar Wavelet Tra...
Image Compression Comparison Using Golden Section Transform, Haar Wavelet Transform and Daubechies D4 Wavelet By Matlab
Gradient of graph
The gradient of a line measures how steep the line is, and can be positive, negative, or zero. The gradient is calculated by taking the change in y over the change in x between two points on the line. If the line is vertical, its gradient cannot be determined. Examples are provided to demonstrate calculating the gradient using points on a line and the formula for change in y over change in x.
Learning objects lo4
- Sound waves are longitudinal waves that propagate in three dimensions through pressure variations caused by particle displacements.
- The speed of sound can be calculated using the bulk modulus and density of the medium using the equation v=√B/ρ.
- The mathematical description of the displacement amplitude of a sound wave is s(x,t)=smcos(kx-ωt+φ), where sm is the maximum displacement, k is the wave number, ω is the angular frequency, and φ is the phase constant.
- The relationships between displacement, pressure, and intensity can be determined from the equations Δp(pressurechange)=Bk smsin(kx-ωt+φ) and I=1/2
Cluster abundances and clustering Can theory step up to precision cosmology?
This document discusses improvements to the Press-Schechter theory for modeling the abundances and clustering of dark matter halos. It proposes that modeling halo collapse as requiring the density to "step up" above a critical density threshold at progressively larger spatial scales provides a better approximation than assuming fully correlated or uncorrelated densities. This "stepping up" approach requires only 2-point statistics and can be applied to non-Gaussian fields. The document also suggests that modeling the distribution of density slopes at peak positions provides a way to match halo counts through an Excursion Set Peaks model.
Day 1b examples
The Extreme Value Theorem states that if a function is continuous on a closed interval, then it has a global maximum and minimum value on that interval. These global extrema can only occur at critical points or endpoints. The document provides an example of finding the global max and min of the function f(x)=2x-x^2 by identifying critical numbers and endpoint values and comparing them.
Day 8 examples
The document discusses continuous growth and decay using the formula P = P0ert, where P is the current value, P0 is the initial value, r is the growth/decay rate, and t is time. It provides examples of using the formula to calculate population growth reaching a target size, the amount of radioactive substance remaining after a given time period, and the half-life of a continuously decaying substance.
Day 2 examples
The document discusses accumulation functions and their properties. An accumulation function F(x) is defined as the definite integral of a continuous function f from 0 to x. F(x) has the same domain as f. The sign convention states that if the integral makes sense for values of x less than the bounds of integration, then F(x) takes on the sign of the integrand f(x). Tables are included to illustrate the graph and values of an example accumulation function.
Day 4a examples
1. The x-intercept of the function y=f(x) is 5, so the x-intercept of y=f(x)^2 is also 5.
2. The coordinates of a point on the graph of y=g(x) are (-3,5), so the coordinates of a point on the graph of y=h(-x) are (3,5).
3. The equation y=-f(x-4) describes a function that is shifted down 4 units and compressed vertically by a factor of 2 compared to the original function f(x).
Day 3b examples
Radical equations contain variables under radical signs. To solve these equations, isolate the radical term on one side by performing the same operations to both sides. Then, square both sides of the equation to remove the radical, which may introduce extraneous solutions that must be checked. Finally, solve the resulting equation using the normal techniques for solving linear equations.
Day 7 examples
This document discusses inverse trigonometric functions and their derivatives. It asks the reader to find the antiderivatives of several inverse trig functions, then asks the reader to find additional antiderivatives of inverse trig functions.
Day 1 examples 2
This document discusses horizontal shifts of functions. It explains that a term like (x - h) shifts a function f(x) right by h units, while (x + h) shifts it left by h units. It provides examples of sketching graphs after horizontal shifts and finding domains and ranges of shifted functions. The document also covers describing shifted functions in words and finding equations of translated absolute value graphs.
Day 7 examples
This document discusses finding the slope of a tangent line at a point on a curve, finding points where tangent lines are horizontal or vertical, and proving the power rule for rational exponents.
Day 4 examples
The document discusses strategies for verifying identities in trigonometry. It provides examples of trigonometric identities to verify, such as sin csc = 1. It recommends working with the more complicated side of the identity and writing all terms with a common denominator to show the left and right sides are equal. Simpler expressions can replace more complicated combinations to verify the identity.
Day 1 examples
The Fundamental Theorem of Calculus states that integrating the derivative of a function over an interval gives the total change in the function over that interval, or the integral of a derivative equals the total change in its parent function. The document then provides examples of using the Fundamental Theorem of Calculus to evaluate integrals and discusses properties like the constant multiple rule, additive interval rule, sum and difference rule, and inequality rule.
Day 4 examples 2
This mathematical expression represents a simple linear equation with one variable, x. The equation is -x + 4, meaning that subtracting x from 4 will yield the solution. Solving this equation would require subtracting x from both sides to isolate x and determine its value.
Sub notes 1
Exponential functions have the form f(x) = b^x where b is the base. As the exponent x increases from left to right on the x-axis, the output y increases as well, making exponential functions increasing. Exponential functions with a base greater than 1 are always increasing, those with a base between 0 and 1 are always decreasing, and the horizontal axis y=0 is the asymptote.
Day 5 examples
Integration by parts is a technique for evaluating definite integrals of products of functions. It allows for integrals that cannot be solved directly using substitution to be evaluated by repeatedly using the formula that breaks up the integral into terms involving both functions and their derivatives. The formula trades the original integral for integrals of the derivatives of one function multiplied by the other function.
Day 2 examples
The document discusses applying the chain rule and product rule to find antiderivatives and asks whether reversing the chain rule can be used to find antiderivatives. It also questions how to test applying these rules and finds antiderivatives for some functions.
Day 3 examples
Composite functions refer to combining two functions where the output of one acts as the input of the other. The notation used is (f ◦ g)(x) which reads "f composed with g of x", where the inner function g(x) is evaluated first, then substituted into the outer function f(x). Examples show how to evaluate composite functions by first substituting the inner function and then evaluating the outer function.
Day 10 examples
This document discusses finding a particular term in a mathematical expression. It contains symbols and formatting that indicate it is discussing concepts related to combinatorics, binomial coefficients, and other mathematical terms. However, without more context it is difficult to determine the specific concepts or terms being discussed.
New Study Of Gita Dec 01 Dr Shriniwas J Kashalikar
This document summarizes Dr. Shriniwas Janarda Kashalikar's study of the Bhagavad Gita. It describes how the author initially disliked the Gita because he felt it promoted escapism from social problems. Through further study and experiences with social activism, the author came to see the Gita as a text that can transform perspectives and promote universal well-being. The document also addresses common criticisms of the Gita and defenses of studying the text with sincere commitment or shraddha.
World Famous Prayer Interpretation By Dr
[1] This prayer seeks happiness, health, and well-being for all, with no grief.
[2] While some object to prayer seeing it as weakness, the author explains prayers help connect to infinite cosmic powers and remove "blocks" like ego that develop in humans.
[3] Prayers and chanting help reconnect us to the empowering source of consciousness and remove feelings of isolation, reestablishing our link to the greater whole of which we are a part.
C O N C E P T O F H O L I S T I C M E D I C I N E D R
1) Holistic medicine emerges from the realization that different medical disciplines are interconnected rather than separate. It views the human body and health in a unified, multidimensional way.
2) Those who integrate or advocate for dialogue between different medical disciplines fit within the holistic framework. Those who rigidly adhere only to one discipline and oppose holistic medicine do not.
3) Holistic medicine is trans-religious, trans-national, trans-cultural, and not confined to a single intellectual or ideological framework. It aims to understand life in its full complexity by comprehending connections between concepts from different medical disciplines.
More Related Content
Viewers also liked
Day 1b examples
The Extreme Value Theorem states that if a function is continuous on a closed interval, then it has a global maximum and minimum value on that interval. These global extrema can only occur at critical points or endpoints. The document provides an example of finding the global max and min of the function f(x)=2x-x^2 by identifying critical numbers and endpoint values and comparing them.
Day 8 examples
The document discusses continuous growth and decay using the formula P = P0ert, where P is the current value, P0 is the initial value, r is the growth/decay rate, and t is time. It provides examples of using the formula to calculate population growth reaching a target size, the amount of radioactive substance remaining after a given time period, and the half-life of a continuously decaying substance.
Day 2 examples
The document discusses accumulation functions and their properties. An accumulation function F(x) is defined as the definite integral of a continuous function f from 0 to x. F(x) has the same domain as f. The sign convention states that if the integral makes sense for values of x less than the bounds of integration, then F(x) takes on the sign of the integrand f(x). Tables are included to illustrate the graph and values of an example accumulation function.
Day 4a examples
1. The x-intercept of the function y=f(x) is 5, so the x-intercept of y=f(x)^2 is also 5.
2. The coordinates of a point on the graph of y=g(x) are (-3,5), so the coordinates of a point on the graph of y=h(-x) are (3,5).
3. The equation y=-f(x-4) describes a function that is shifted down 4 units and compressed vertically by a factor of 2 compared to the original function f(x).
Day 3b examples
Radical equations contain variables under radical signs. To solve these equations, isolate the radical term on one side by performing the same operations to both sides. Then, square both sides of the equation to remove the radical, which may introduce extraneous solutions that must be checked. Finally, solve the resulting equation using the normal techniques for solving linear equations.
Day 7 examples
This document discusses inverse trigonometric functions and their derivatives. It asks the reader to find the antiderivatives of several inverse trig functions, then asks the reader to find additional antiderivatives of inverse trig functions.
Day 1 examples 2
This document discusses horizontal shifts of functions. It explains that a term like (x - h) shifts a function f(x) right by h units, while (x + h) shifts it left by h units. It provides examples of sketching graphs after horizontal shifts and finding domains and ranges of shifted functions. The document also covers describing shifted functions in words and finding equations of translated absolute value graphs.
Day 7 examples
This document discusses finding the slope of a tangent line at a point on a curve, finding points where tangent lines are horizontal or vertical, and proving the power rule for rational exponents.
Day 4 examples
The document discusses strategies for verifying identities in trigonometry. It provides examples of trigonometric identities to verify, such as sin csc = 1. It recommends working with the more complicated side of the identity and writing all terms with a common denominator to show the left and right sides are equal. Simpler expressions can replace more complicated combinations to verify the identity.
Day 1 examples
The Fundamental Theorem of Calculus states that integrating the derivative of a function over an interval gives the total change in the function over that interval, or the integral of a derivative equals the total change in its parent function. The document then provides examples of using the Fundamental Theorem of Calculus to evaluate integrals and discusses properties like the constant multiple rule, additive interval rule, sum and difference rule, and inequality rule.
Day 4 examples 2
This mathematical expression represents a simple linear equation with one variable, x. The equation is -x + 4, meaning that subtracting x from 4 will yield the solution. Solving this equation would require subtracting x from both sides to isolate x and determine its value.
Sub notes 1
Exponential functions have the form f(x) = b^x where b is the base. As the exponent x increases from left to right on the x-axis, the output y increases as well, making exponential functions increasing. Exponential functions with a base greater than 1 are always increasing, those with a base between 0 and 1 are always decreasing, and the horizontal axis y=0 is the asymptote.
Day 5 examples
Integration by parts is a technique for evaluating definite integrals of products of functions. It allows for integrals that cannot be solved directly using substitution to be evaluated by repeatedly using the formula that breaks up the integral into terms involving both functions and their derivatives. The formula trades the original integral for integrals of the derivatives of one function multiplied by the other function.
Day 2 examples
The document discusses applying the chain rule and product rule to find antiderivatives and asks whether reversing the chain rule can be used to find antiderivatives. It also questions how to test applying these rules and finds antiderivatives for some functions.
Day 3 examples
Composite functions refer to combining two functions where the output of one acts as the input of the other. The notation used is (f ◦ g)(x) which reads "f composed with g of x", where the inner function g(x) is evaluated first, then substituted into the outer function f(x). Examples show how to evaluate composite functions by first substituting the inner function and then evaluating the outer function.
Day 10 examples
This document discusses finding a particular term in a mathematical expression. It contains symbols and formatting that indicate it is discussing concepts related to combinatorics, binomial coefficients, and other mathematical terms. However, without more context it is difficult to determine the specific concepts or terms being discussed.
New Study Of Gita Dec 01 Dr Shriniwas J Kashalikar
This document summarizes Dr. Shriniwas Janarda Kashalikar's study of the Bhagavad Gita. It describes how the author initially disliked the Gita because he felt it promoted escapism from social problems. Through further study and experiences with social activism, the author came to see the Gita as a text that can transform perspectives and promote universal well-being. The document also addresses common criticisms of the Gita and defenses of studying the text with sincere commitment or shraddha.
World Famous Prayer Interpretation By Dr
[1] This prayer seeks happiness, health, and well-being for all, with no grief.
[2] While some object to prayer seeing it as weakness, the author explains prayers help connect to infinite cosmic powers and remove "blocks" like ego that develop in humans.
[3] Prayers and chanting help reconnect us to the empowering source of consciousness and remove feelings of isolation, reestablishing our link to the greater whole of which we are a part.
C O N C E P T O F H O L I S T I C M E D I C I N E D R
1) Holistic medicine emerges from the realization that different medical disciplines are interconnected rather than separate. It views the human body and health in a unified, multidimensional way.
2) Those who integrate or advocate for dialogue between different medical disciplines fit within the holistic framework. Those who rigidly adhere only to one discipline and oppose holistic medicine do not.
3) Holistic medicine is trans-religious, trans-national, trans-cultural, and not confined to a single intellectual or ideological framework. It aims to understand life in its full complexity by comprehending connections between concepts from different medical disciplines.
Viewers also liked (20)
New Study Of Gita Dec 01 Dr Shriniwas J Kashalikar
New Study Of Gita Dec 01 Dr Shriniwas J Kashalikar
C O N C E P T O F H O L I S T I C M E D I C I N E D R
C O N C E P T O F H O L I S T I C M E D I C I N E D R
More from jchartiersjsd
Combs perms review pascals
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
Day 8 examples u7w14
This document contains 5 problems involving finding terms in expansions of polynomials. The problems involve finding specific terms that contain a given power of x in expansions of polynomials such as (3x^4 - 1)^9, (-x^3 + 2)^6, (x + 1)^3x, (x + 1)^x, and determining the value of m if one term in the expansion of (2x - m)^7 is -262500x^2y^5.
Day 7 examples u7w14
The document discusses binomial expansion, which is the process of multiplying out terms with two variables according to their power using the binomial theorem. It provides examples of expanding binomial expressions like (x + y)2, (x + y)3, and (x + y)4. It also notes that the sum of the exponents in each term equals the overall power, and the number of terms is always one more than the power. Finally, it provides the binomial theorem for expanding any binomial expression and finding a particular term.
Day 4 examples u7w14
This document discusses how to calculate arrangements when some items must be together or apart. It explains that when items need to be together, they should be counted as a single item to reduce the total items being arranged. Then the total number of arrangements is calculated by finding the total possible arrangements and subtracting the arrangements that do not satisfy the constraints of certain items being together or apart. Examples provided include arranging people in a row when some must or cannot sit together and arranging books on a shelf keeping books of each subject together.
Day 3 examples u7w14
Permutations refer to arrangements of objects in a definite order. Some key points:
- Permutations are represented by "nPn" where n is the total number of objects and r is the number being arranged.
- Permutations are used to calculate possibilities like license plates, phone numbers, and locker combinations.
- Restrictions like starting/ending conditions or requiring alternating arrangements reduce the number of possible permutations.
- Objects that are identical only count once toward the total number of permutations rather than being distinguishable.
Day 2 examples u7w14
Factorial notation represents the product of all positive integers less than or equal to the given number. For example, 5! = 5 x 4 x 3 x 2 x 1 and 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. The document also provides examples of simplifying factorials without a calculator by using properties such as 5! + 4! = 6 x 4! and (k + 1)! + k! = (k + 2)k!.
Day 1 examples u7w14
This document provides examples and explanations of the fundamental counting principle and addition counting principle to solve combinatorics problems. It gives 8 examples of using the fundamental counting principle to count the number of possible outcomes of independent events. These include counting the number of volleyball shoe combinations, outfits that can be created from different clothing items, ways to select committees from groups of people, and 3-digit numbers with no repeating digits. It also provides 5 examples of using the addition counting principle to count outcomes when events are dependent, such as selecting a president and vice president of opposite sexes from a group.
Day 7 examples u6w14
This document discusses graphing composite functions. It provides examples of determining the composite functions f(g(x)) and g(f(x)) for various functions f(x) and g(x), sketching the graphs of the composite functions, and stating their domains. It also gives examples of determining possible functions f(x) and g(x) that satisfy given composite functions.
Day 5 examples u6w14
1. The document discusses composite functions, which involve combining two functions f(x) and g(x) where the output of one is used as the input of the other. It provides examples of evaluating composite functions using tables and graphs.
2. Key steps for evaluating composite functions are: 1) Substitute the inner function into the outer function and 2) Simplify the expression. Order matters as f(g(x)) and g(f(x)) may have different values.
3. Examples are worked through to find composite functions given basic functions like f(x) = x + 1 and g(x) = 2x as well as more complex rational functions.
Day 4 examples u6w14
The graph is a linear function with a domain of all real numbers and a range of real numbers greater than or equal to 3. The graph is a line with a y-intercept of 3 that increases at a rate of 1 as x increases.
Day 3 examples u6w14
Rational functions are functions of the form f(x) = p(x)/q(x) where p(x) and q(x) are polynomials. For example, comparing rational functions like 2x/(x^2 - 4) and (x-1)/(x+1). Horizontal asymptotes of rational functions occur when the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator.
Day 2 examples u6w14
This document discusses combining functions by graphing. When two functions f(x) and g(x) are combined, their graphs are overlayed on the same coordinate plane. The result is a new combined function where the output is determined by applying both functions f(x) and g(x) to the same input x.
Day 1 examples u6w14
This document discusses how to find the sum, difference, product, and quotient of functions. The sum of functions is found by adding the y-coordinates of each function. The difference is found by subtracting the y-coordinates. The product is represented as h(x) = f(x)g(x) and the quotient is represented as h(x) = f(x)/g(x). Examples are provided for adding and subtracting functions.
Mental math test outline
The document outlines a mental math test covering polynomials. It includes short answer questions testing long division, synthetic division, the remainder theorem, and finding the degree, leading coefficient, and y-intercept of polynomials. The test also covers matching graphs to polynomial equations and word problems involving fully factoring polynomials and two graphs. Multiple choice questions will require explaining solutions, while long answer questions involve fully factoring polynomials and word problems.
Day 8 examples u5w14
The document contains two polynomial word problems. The first asks to write a function V(x) to express the volume of a box with dimensions x, x+2, x+10 in terms of x, and find possible x values if the volume is 96 cm^3. The second problem describes a block of ice that is initially 3 ft by 4 ft by 5 ft, and asks to write a function to model reducing each dimension by the same amount to reach a volume of 24 ft^3, and determine how much to remove from each dimension.
Day 7 examples u5w14
The document provides 3 polynomial word problems: 1) finding the equation for a polynomial given its graph f(x) = -(x - 2)2(x + 1), 2) determining the polynomial P(x) when divided by (x - 3) with a quotient of 2x^2 + x - 6 and remainder of 4, and 3) finding the value of a if (x - 2) is a factor of ax^3 + 4x^2 + x - 2. It also gives a 4th problem of determining the value of k when 2x^3 + kx^2 - 3x + 2 is divided by x - 2 with a remainder of 4.
Day 5 examples u5w14
Polynomial functions are described by their degree and have certain characteristics. The graph of a polynomial is smooth and continuous without sharp corners. Odd degree polynomials rise on the left and fall on the right, while even degree polynomials rise on both sides. The number of x-intercepts and local maxima/minima are limited by the degree. Polynomials can be matched based on their degree, leading coefficient, even/odd nature, and number of x-intercepts and local extrema. The x-intercepts of a polynomial correspond to the roots of the equation, and a repeated root indicates a zero of higher multiplicity which affects the graph.
More from jchartiersjsd (20)
Day 3 examples a
- 1. Stretching and Compressing Compression
- 2. Compression 1 2 1 2
- 3. vertically compressed by a factor of 1/3
- 4. g(x) = 2f(1/4x) Graph: w(x) = -3v(2x) Graph: s(x) = 1/3p(-2x)