64-63 4 5 6-2-4-5-6+The graph above is a transformation of the function f(x) = |x|.Write an formula for the function graphed above:g(x) =

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Answered: -6 -2 2 3 45 6 -2 -5- The graph above…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.6: Transformations Of Functions

Problem 47E

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Subject: Calculus from Mathematics for Secondary School Teachers/ Measurement And Polynomials Calculus from Mathematics for Secondary School Teachers/ Measurement And Polynomials Your Turn 3. Let g ( x ) = x h ( x ) = g ( x − 2) . (a) (b) (c) (d) 3 + 6 x 2 − 2 x − 15 and h( x ) = x 3 − 14 x + 5 be as above, and recall that Using a graphing device, graph both g x ) and h( x). In terms of graphing transformations, how does one obtain the graph of h (x) from the graph of g (x) ? Given the x-intercepts of g(x), how could you ﬁnd the x-intercepts for the graph of h (x)? What is the inﬂection point for the graph of h(x)? Estimate the sum of the x-intercepts for the graph of h (x) . 0
Population Growth: The growth G of a population over a week is a function of the population size n at the beginning of the week. If both n and G are measured in thousands of animals, the formula is G=0.25n2+5n, a. Make a graph of G versus n. Include values of n up to 25 thousand animals. b. Use functional notation to express the growth over a week if the population at the beginning is 4 thousand animals, and then calculate that value. c. Calculate G(22) and explain in practical terms what your answer means. d. For what values of n is the function G increasing? Determine whether the graph is concave up or concave down for these values, and explain in practical terms what this means.
Geometry You want to make an open box from a rectangular piece of material, 15 centimeters by 9 centimeters, by cutting equal squares from the corners and turning up the sides. (a) Let x represent the side length of each of the squares removed. Draw a diagram showing the squares removed from the original piece of material and the resulting dimensions of the open box. (b) Use the diagram to write the volume V of the box as a function of x. Determine the domain of the function. (c) Sketch the graph of the function and approximate the dimensions of the box that yield a maximum volume. (d) Find values of x such that V=56. Which of these values is a physical impossibility in the construction of the box? Explain.

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-6 -2 2 3 45 6 -2 -5- The graph above is a transformation of the function f(x) = |x|.