College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter3: Functions
3.1 Functions And Function Notation 3.2 Domain And Range 3.3 Rates Of Change And Behavior Of Graphs 3.4 Composition Of Functions 3.5 Transformation Of Functions 3.6 Absolute Value Functions 3.7 Inverse Functions Chapter Questions Section3.5: Transformation Of Functions
Problem 1TI: The function h(t)=4.9t2+30t gives the height h of a ball (in meters) thrown upward from the ground... Problem 2TI: Given the function f(x)=x , graph the original function f(x) and the transformation g(x)=f(x+2) on... Problem 3TI: Given f(x)=|x| , sketch a graph of h(x)=f(x-2)+4 . Problem 4TI: Write a formula for a transformation of the toolkit reciprocal function f(x)=1x that shifts the... Problem 5TI: Reflect the graph of f(x)=|x1| a. vertically and b. horizontally. Problem 6TI: A function f(x) is given as Table 9. Create a table for the functions below. g(x)=f(x) h(x)=f(x) Problem 7TI: Given the toolkit function f(x)=x2 , graph g(x)=-f(x)andh(x)=f(x) . Take note of any surprising... Problem 8TI: Is the function f(s)=s4+3s2+7 even, odd, or neither? Problem 9TI: A function f is given as Table 12. Create a table for the function g(x)=34f(x) . Problem 10TI: Write the formula for the function that we get when we stretch the identity toolkit function by a... Problem 11TI: Write a formula for the toolkit square root function horizontally stretched by a factor of 3. Problem 1SE: When examining the formula of a function that is the result of multiple transformations, how can you... Problem 2SE: When examining the formula of a function that is the result of multiple transformations, how can you... Problem 3SE: When examining the formula of a function that is the result of multiple transformations, how can you... Problem 4SE: When examining the formula of a function that is the result of multiple transformations, how can you... Problem 5SE: How can you determine whether a function is odd or even from the formula of the function? Problem 6SE: For the following exercises, write a formula for the function obtained when the graph is shifted as... Problem 7SE: For the following exercises, write a formula for the function obtained when the graph is shifted as... Problem 8SE: For the following exercises, write a formula for the function obtained when the graph is shifted as... Problem 9SE: For the following exercises, write a formula for the function obtained when the graph is shifted as... Problem 10SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 11SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 12SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 13SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 14SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 15SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 16SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 17SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 18SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 19SE: For the following exercises, describe how the graph of the function is a transformation of the graph... Problem 20SE: For the following exercises, determine the interval(s) on which the function is increasing and... Problem 21SE: For the following exercises, determine the interval(s) on which the function is increasing and... Problem 22SE: For the following exercises, determine the interval(s) on which the function is increasing and... Problem 23SE: For the following exercises, determine the interval(s) on which the function is increasing and... Problem 24SE: For the following exercises, use the graph of f(x)=2X shown in Figure 31 to sketch a graph of each... Problem 25SE: For the following exercises, use the graph of f(x)=2X shown in Figure 31 to sketch a graph of each... Problem 26SE: For the following exercises, use the graph of f(x)=2X shown in Figure 31 to sketch a graph of each... Problem 27SE: For the following exercises, sketch a graph of the function as a transformation of the graph of one... Problem 28SE: For the following exercises, sketch a graph of the function as a transformation of the graph of one... Problem 29SE: For the following exercises, sketch a graph of the function as a transformation of the graph of one... Problem 30SE: For the following exercises, sketch a graph of the function as a transformation of the graph of one... Problem 31SE: Tubular representations for the functions f, g and h are given below. Write g(x) and h(x) as... Problem 32SE: Tubular representations for the functions f, g and h are given below. Write g(x) and h(x) as... Problem 33SE: For the following exercises, write an equation for each graphed function by using transformation of... Problem 34SE: For the following exercises, write an equation for each graphed function by using transformation of... Problem 35SE: For the following exercises, write an equation for each graphed function by using transformation of... Problem 36SE: For the following exercises, write an equation for each graphed function by using transformation of... Problem 37SE: For the following exercises, write an equation for each graphed function by using transformation of... Problem 38SE: For the following exercises, write an equation for each graphed function by using transformation of... Problem 39SE: For the following exercises, write an equation for each graphed function by using transformation of... Problem 40SE: For the following exercises, write an equation for each graphed function by using transformation of... Problem 41SE: For the following exercises, use the graphs of transformations of the square root function to find a... Problem 42SE: For the following exercises, use the graphs of transformations of the square root function to find a... Problem 43SE: Y1yg For the following exercises, use the graphs of the transformed toolkit functions to write a... Problem 44SE: For the following exercises, use the graphs of the transformed toolkit functions to write a formula... Problem 45SE: For the following exercises, use the graphs of the transformed toolkit functions to write a formula... Problem 46SE: For the following exercises, use the graphs of the transformed toolkit functions to write a formula... Problem 47SE: For the following exercises, determine whether the function is odd, even, or neither. f(x)=3x4 Problem 48SE: For the following exercises, determine whether the function is odd, even, or neither. g(x)=x Problem 49SE: For the following exercises, determine whether the function is odd, even, or neither. h(x)=1x+3x Problem 50SE: For the following exercises, determine whether the function is odd, even, or neither. f(x)=(x2)2 Problem 51SE: For the following exercises, determine whether the function is odd, even, or neither. g(x)=2x4 Problem 52SE: For the following exercises, determine whether the function is odd, even, or neither. h(x)=2xx3 Problem 53SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 54SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 55SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 56SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 57SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 58SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 59SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 60SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 61SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 62SE: For the following exercises, describe how the graph of each function is a transformation of the... Problem 63SE: For the following exercises, write a formula for the function g that results when the graph of a... Problem 64SE: For the following exercises, write a formula for the function g that results when the graph of a... Problem 65SE: For the following exercises, write a formula for the function g that results when the graph of a... Problem 66SE: For the following exercises, write a formula for the function g that results when the graph of a... Problem 67SE: For the following exercises, write a formula for the function g that results when the graph of a... Problem 68SE: For the following exercises, write a formula for the function g that results when the graph of a... Problem 69SE: For the following exercises, write a formula for the function g that results when the graph of a... Problem 70SE: For the following exercises, describe how the formula is a transformation of a toolkit function.... Problem 71SE: For the following exercises, describe how the formula is a transformation of a toolkit function.... Problem 72SE: For the following exercises, describe how the formula is a transformation of a toolkit function.... Problem 73SE: For the following exercises, describe how the formula is a transformation of a toolkit function.... Problem 74SE: For the following exercises, describe how the formula is a transformation of a toolkit function.... Problem 75SE: For the following exercises, describe how the formula is a transformation of a toolkit function.... Problem 76SE: the following exercises, describe how the formula is a transformation of a toolkit function. Then... Problem 77SE: For the following exercises, describe how the formula is a transformation of a toolkit function.... Problem 78SE: For the following exercises, use the graph in Figure 32 to sketch the given transformations. 78.... Problem 79SE: sFor the following exercises, use the graph in Figure 32 to sketch the given transformations.... Problem 80SE: For the following exercises, use the graph in Figure 32 to sketch the given transformations.... Problem 81SE: For the following exercises, use the graph in Figure 32 to sketch the given transformations.... Problem 5SE: How can you determine whether a function is odd or even from the formula of the function?
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Use the derivative f’(x)=x^2(x-5)(x+5) to determine The local maxima and minimal of f and the intervals of increase and decrease. Sketch a possible graph of f (f is not Unique)
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
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