Polynomia ls
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This document defines and provides examples of polynomials. A polynomial is a function with real number coefficients and whole number exponents. To analyze a polynomial, you find its zeros, degree, and left and right end behavior, then graph it. The degree determines the direction of the graph's arrows. Even degrees have up arrows, odd degrees have one up and one down, and negative degrees reverse the arrows. The document also defines degree as the sum of exponents and root behavior as how a line passes through zeros. An example polynomial is worked through to demonstrate.
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This document provides steps for graphing polynomial equations. It explains that you graph the points indicated by the factors in the equation, with positive or negative signs depending on whether it is positive or negative in the equation. It then defines different types of lines that can be graphed - pass through, bounce off, or squiggle through - depending on the exponents of the factors. The degree of the polynomial, whether even or odd, determines whether the ends of the line go up or down. Examples are provided to demonstrate these steps.
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The document discusses graphs of rational functions and how to analyze them. It covers identifying vertical and horizontal asymptotes analytically by finding values where the denominator is zero or analyzing behavior as x approaches positive/negative infinity. Examples show graphing rational functions by plotting points near asymptotes and connecting them, confirming asymptotes numerically. Key steps are finding intercepts and asymptotes, making a table near asymptotes, and graphing points and asymptotes. The reader is assigned practice problems applying these skills.
Algebra in Real Life
is used. Mathematics is applied in day to day life, so we can now review the concepts of Algebra and its uses in daily life. Here in our work we have made a small split up of items in a bag while shopping. Basic Algebra is where we finally put the algebra in pre-algebra. The concepts taught here will be used in every math class you take from here on. Well introduce you to some exciting stuff like drawing graphs and solving complicated equations. Since we are learning Algebra, Geometry in the school days. But the is a real life application of Algebra which is used in Geometry. Now a days the social media has improved a lot. We cant able to solve those figured puzzles, hence we can solve them by using algebraic equations. S. Ambika | R. Mythrae | S. Saranya | K. Selvanayaki "Algebra in Real Life" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd21517.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/algebra/21517/algebra-in-real-life/s-ambika
Graphing polynomial functions
The end behavior of a polynomial function is determined by the degree of the equation, with even degrees opening up and odd degrees opening in opposite directions. The behavior at points on the x-axis depends on whether the power of a term is even, resulting in a bounce, odd resulting in a squiggle, or one resulting in a pass through.
Graphing polynomial functions
The end behavior of a polynomial function is determined by the degree of the equation, with even degrees opening up and odd degrees opening in opposite directions. The behavior at points on the x-axis depends on whether the power of a term is even, resulting in a bounce, odd resulting in a squiggle, or one resulting in a pass through.
Graphing polynomials
The document discusses how to graph polynomials by determining the x-intercepts from the zeros of the polynomial, the y-intercept, and the behavior at infinity using the leading coefficient test. It provides details on how the multiplicity of zeros relates to whether x-intercepts cross or touch the x-axis, and whether the graph is flat at those points. An example graphing the polynomial f(x)=x^5-5x^4+10x^3-10x^2+5x-40 is worked through step-by-step.
Skill31 b graphinglinesandformsof equations
This lesson teaches how to graph equations in y = mx + b form and also teaches three forms of the equation of a line.
Rational functions
Rational functions are any functions that can be written as the ratio of two polynomial functions. There are two types of asymptotes for rational functions: vertical asymptotes, which occur at the zeros of the denominator and cannot be crossed, and horizontal asymptotes, which can be crossed. To find the vertical and horizontal asymptotes of a rational function, you examine the degrees of the numerator and denominator polynomials. The domain of a rational function is the set of x-values that make the function defined, while the range is the set of possible y-values produced by the function.
Similar to Polynomia ls (20)
Mathematics power point presenttation on the topic
Mathematics power point presenttation on the topic
Polynomia ls
- 1. PolynomiaLs- Madison Lee.
- 2. explanatiOn- A polynomial is a function of the form, all real numbers and all the exponents are all whole numbers. First you are given an equation you are to find the zeros, degree, left and right end behavior and after finding all of the following you graph it. If your degree is an odd number then one arrow points up and one arrow points down. If your degree is an even number then your arrows are both going up. If your degree is a negative and an a even number both arrows go down. If your degree is a negative and an odd number then one arrow is up and one arrow is down.
- 3. DefinitiOns- A degree is the exponents added together in an equation. Ex- (x+1)2 (x-2) (x-3) The degree would be 4 because in the first parenthesis there is 2, in the second there is 1 and in the third there is 1. Root Behavior is the ways the line passes through the x-int. There are 3 different ways the line can pass through the x- int. The three ways are pass through, bounce off and squiggle through.
- 4. ExampLe- Example- Y= 2(x+4)(x-5)2 Zeros(include multiplicity) -4 Mult of 2,5. Degree- 3 (odd) Left EB- down Right EB- up So the arrows in your graph, one would be going up and one would be going down.