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11th sept 2014
This 3 sentence document simply repeats the date "September 11, 2014" three times on three different lines. It does not provide any other context or information.
3.2 6th feb 2013
The document discusses reflections of functions across the x-axis and y-axis. Reflecting across the y-axis causes the x-values to become opposite, resulting in the function y=f(-x). Reflecting across the x-axis causes the y-values to become opposite, resulting in the function y=-f(x). The document provides examples of determining the reflected point for a given point on a function, and instructs the reader to sketch both the original and reflected graphs.
30th november 2012
The document appears to be a log of timestamps from November 30, 2012 showing times between 2:31 PM and 3:20 PM. There are 7 entries showing times at 2:31 PM, 2:39 PM, 2:44 PM, 2:47 PM, 3:01 PM, 3:09 PM, and 3:20 PM on that date.
Pc12 sol c08_8-6
This document provides examples and explanations of using Pascal's triangle to expand binomial expressions. It shows how to:
1) Expand binomial expressions like (x + 1)5 and (x - y)8 using the appropriate row of Pascal's triangle as coefficients.
2) Determine missing coefficients in expansions like (x + y)7.
3) Compare directly multiplying factors to using the binomial theorem to expand expressions like (x - 5)4.
4) Expand various binomial expressions like (x + 2)6, (x2 - 3)5, and (-2 + 2x)4 by applying the binomial theorem.
27th september 2012 summ and difference identities
This document discusses sum and difference identities for trigonometric functions. It explains that the sum and difference of two trig functions can be rewritten in terms of a single trig function using trigonometric identities. Examples are provided to show how trig identities can be used to simplify expressions involving sums or differences of trig functions into a single trig function of the sum or difference of the angles.
Trig identities #1 solutions
The document is a notebook on trigonometric identities from November 27, 2012. It covers over 25 pages and explores over a dozen important trig identities including the sum, difference, double-angle, and half-angle formulas as well as identities involving trig functions of multiples of an angle. Examples are provided to demonstrate how to use the identities to simplify trigonometric expressions.
8th sept. 2014
This document appears to be a series of 3 short sections, each labeled 1.3 and dated September 08, 2014. While no other contextual information is provided, the document seems to contain 3 brief pieces of information or entries from that date.
8.3 combinations 21st december 2012
This document discusses combinations and provides examples to distinguish them from permutations. Combinations refer to situations where order does not matter when selecting objects without arranging them. The key formula for combinations is provided as nCr = n!/(r!(n-r)!). Examples are given to calculate combinations and identify patterns. Practice problems are assigned for combinations.
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11th sept 2014
This 3 sentence document simply repeats the date "September 11, 2014" three times on three different lines. It does not provide any other context or information.
3.2 6th feb 2013
The document discusses reflections of functions across the x-axis and y-axis. Reflecting across the y-axis causes the x-values to become opposite, resulting in the function y=f(-x). Reflecting across the x-axis causes the y-values to become opposite, resulting in the function y=-f(x). The document provides examples of determining the reflected point for a given point on a function, and instructs the reader to sketch both the original and reflected graphs.
30th november 2012
The document appears to be a log of timestamps from November 30, 2012 showing times between 2:31 PM and 3:20 PM. There are 7 entries showing times at 2:31 PM, 2:39 PM, 2:44 PM, 2:47 PM, 3:01 PM, 3:09 PM, and 3:20 PM on that date.
Pc12 sol c08_8-6
This document provides examples and explanations of using Pascal's triangle to expand binomial expressions. It shows how to:
1) Expand binomial expressions like (x + 1)5 and (x - y)8 using the appropriate row of Pascal's triangle as coefficients.
2) Determine missing coefficients in expansions like (x + y)7.
3) Compare directly multiplying factors to using the binomial theorem to expand expressions like (x - 5)4.
4) Expand various binomial expressions like (x + 2)6, (x2 - 3)5, and (-2 + 2x)4 by applying the binomial theorem.
27th september 2012 summ and difference identities
This document discusses sum and difference identities for trigonometric functions. It explains that the sum and difference of two trig functions can be rewritten in terms of a single trig function using trigonometric identities. Examples are provided to show how trig identities can be used to simplify expressions involving sums or differences of trig functions into a single trig function of the sum or difference of the angles.
Trig identities #1 solutions
The document is a notebook on trigonometric identities from November 27, 2012. It covers over 25 pages and explores over a dozen important trig identities including the sum, difference, double-angle, and half-angle formulas as well as identities involving trig functions of multiples of an angle. Examples are provided to demonstrate how to use the identities to simplify trigonometric expressions.
8th sept. 2014
This document appears to be a series of 3 short sections, each labeled 1.3 and dated September 08, 2014. While no other contextual information is provided, the document seems to contain 3 brief pieces of information or entries from that date.
8.3 combinations 21st december 2012
This document discusses combinations and provides examples to distinguish them from permutations. Combinations refer to situations where order does not matter when selecting objects without arranging them. The key formula for combinations is provided as nCr = n!/(r!(n-r)!). Examples are given to calculate combinations and identify patterns. Practice problems are assigned for combinations.
5th sept 1.2
This document is a log of entries from September 5th, 2014. It contains 5 brief entries all dated September 5th, 2014 with increasing numbering from 1 to 5. The log entries do not contain any other details.
Quiz solultions absolute value
This document provides solutions to an absolute value quiz. It explains the steps to solve absolute value equations such as |x-3| = 5 by splitting it into cases of x-3 ≥ 0 and x-3 < 0. It also shows how to evaluate and simplify expressions involving absolute values, such as |x| + 4, by considering x as either positive or negative.
Absolute value 1
The document defines absolute value as the non-negative value of a real number without regard to its sign. It provides examples of calculating the absolute value of numbers and ordering numbers by their absolute values. Absolute value represents the distance of a number from zero on a number line. The document suggests absolute values are useful and provides homework problems for further practice.
6th december 2012
The document discusses logarithmic functions and their properties when graphed. It explores the relationship between logarithmic and exponential functions by showing their inverse graphical relationship. Examples are shown of logarithmic functions graphed along with their corresponding exponential functions to illustrate how changing variables in one function results in a reflection change in the other graphed function.
Solutions 3-1
This document contains solutions to exercises about translating graphs of functions. It includes:
1) Examples of translating the graph of y = |x| by different amounts, and writing the equations of the translated graphs.
2) Describing how graphs are translated based on the equations of the form y = f(x - h) or y - k = f(x).
3) Sketching translated graphs on grids and stating their domains and ranges.
4) An example of finding the coordinates of the image of a point on a graph after it is translated.
5) Discussion of how vertical and horizontal asymptotes are affected by translation, and writing the equations of asymptotes for a
4th sept 2014 1.1
This four paragraph document appears to be notes from September 4th, 2014 as each paragraph is labeled "4th sept 1.1" and includes the date. However, there is no other contextual information provided in the document to understand its purpose or overall content beyond the recording of this labeling system and date.
4.4 12th feb 2013
The document appears to be a series of text messages between two individuals discussing plans to meet on February 12, 2013. They mention confirming details like the time and location of their meeting, with one person saying they will be there around 3:13 PM that day.
4.3 25th october 2012
The document introduces composite functions, which are formed by placing one function inside another. To evaluate a composite function f(g(x)), the inner function g(x) is evaluated first, and the result is substituted into the outer function f(x). It provides examples of evaluating various composite functions step-by-step. Key concepts covered include working from the inside out, and that the composition f(g(x)) is not the same as the multiplication f * g(x). Homework problems are assigned.
6th october 2014
This document contains 3 short entries dated October 06, 2014 that are all labeled "6th october 2014". The document appears to be a log or record with multiple brief entries made on the same date.
3rd october 2014
This document is a list of dates, all occurring on October 3rd, 2014. Each entry repeats the date and contains a page number. There are 9 total entries in the list, each with the same date but incrementing page numbers from 1 through 9.
2nd october 2014
This document is a log of dates from October 2nd, 2014. It contains 5 entries all with the same date of October 2nd, 2014 listed 5 separate times.
1st october 2014
This document appears to be a log of dates from October 1st, 2014. It contains four entries all with the date October 1st, 2014 listed. The document provides a brief record of dates but does not include any other contextual information.
30th sept 2014
This document is a series of 8 entries all with the date of September 30, 2014. Each entry contains only the date with no other text or information provided.
25th sept 2014
The document is dated September 25, 2014. It appears to be a brief one paragraph document that does not provide much context or details. The date is the only substantive information given.
25th sept 2014
The document is dated September 25, 2014. It appears to be a brief one paragraph document that does not provide much context or details. The date is the only substantive information given.
24th sept 2014
This document is a record of events from September 24, 2014. It consists of 7 entries all with the same date of September 24, 2014 listed at the top, suggesting some type of daily log or journal was being kept for that date.
23rd sept. 2014
This document is a series of 7 entries all dated September 23, 2014 without any other notable information provided. Each entry simply states the date of September 23, 2014.
22nd sept 2014
This four sentence document repeats the date September 22, 2014 four times without providing any additional context or information. The document states the same date, September 22, 2014, in each of its four sentences without elaborating on the significance of the date or including any other details.
18th sept 2014
This document is a record of dates, containing six identical entries of "September 18, 2014" with no other text or context provided. Each entry is on its own line and labeled with "18th sept 2014" and a number.
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5th sept 1.2
This document is a log of entries from September 5th, 2014. It contains 5 brief entries all dated September 5th, 2014 with increasing numbering from 1 to 5. The log entries do not contain any other details.
Quiz solultions absolute value
This document provides solutions to an absolute value quiz. It explains the steps to solve absolute value equations such as |x-3| = 5 by splitting it into cases of x-3 ≥ 0 and x-3 < 0. It also shows how to evaluate and simplify expressions involving absolute values, such as |x| + 4, by considering x as either positive or negative.
Absolute value 1
The document defines absolute value as the non-negative value of a real number without regard to its sign. It provides examples of calculating the absolute value of numbers and ordering numbers by their absolute values. Absolute value represents the distance of a number from zero on a number line. The document suggests absolute values are useful and provides homework problems for further practice.
6th december 2012
The document discusses logarithmic functions and their properties when graphed. It explores the relationship between logarithmic and exponential functions by showing their inverse graphical relationship. Examples are shown of logarithmic functions graphed along with their corresponding exponential functions to illustrate how changing variables in one function results in a reflection change in the other graphed function.
Solutions 3-1
This document contains solutions to exercises about translating graphs of functions. It includes:
1) Examples of translating the graph of y = |x| by different amounts, and writing the equations of the translated graphs.
2) Describing how graphs are translated based on the equations of the form y = f(x - h) or y - k = f(x).
3) Sketching translated graphs on grids and stating their domains and ranges.
4) An example of finding the coordinates of the image of a point on a graph after it is translated.
5) Discussion of how vertical and horizontal asymptotes are affected by translation, and writing the equations of asymptotes for a
4th sept 2014 1.1
This four paragraph document appears to be notes from September 4th, 2014 as each paragraph is labeled "4th sept 1.1" and includes the date. However, there is no other contextual information provided in the document to understand its purpose or overall content beyond the recording of this labeling system and date.
4.4 12th feb 2013
The document appears to be a series of text messages between two individuals discussing plans to meet on February 12, 2013. They mention confirming details like the time and location of their meeting, with one person saying they will be there around 3:13 PM that day.
4.3 25th october 2012
The document introduces composite functions, which are formed by placing one function inside another. To evaluate a composite function f(g(x)), the inner function g(x) is evaluated first, and the result is substituted into the outer function f(x). It provides examples of evaluating various composite functions step-by-step. Key concepts covered include working from the inside out, and that the composition f(g(x)) is not the same as the multiplication f * g(x). Homework problems are assigned.
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