Absolute Value Transformations Problem: Figure 1-6h shows the graph of f(x) = 0.5(x 2)2

Chapter 1, Problem 7

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Absolute Value Transformations Problem: Figure 1-6h shows the graph of f(x) = 0.5(x 2)2 4.5 in the domain 2 x Figure 1-6h a. Plot the graph of y1 = f(x). On the same screen, plot y2 = |f(x)| using thick style. Sketch the result and describe how this transformation changes the graph of f. b. Deactivate y2. On the same screen as y1, plot the graph of y3 = f(|x|) using thick style. Sketch the result and describe how this transformation changes the graph of f. c. Use the equation of function f to find the value of |f(3)| and the value of f(|3|). Show that both results agree with your graphs in parts a and b. Explain why 3 is in the domain of f(|x|) although it is not in the domain of f itself. d. Figure 1-6i shows the graph of a function g, but you dont know the equation. On a copy of this figure, sketch the graph of y = |g(x)|, using the conclusion you reached in part a. On another copy of this figure, sketch the graph of y = g(|x|), using the conclusion you reached in part b. Figure 1-6i