Even Function and Odd Function Problem: Figure 1-6j shows the graph of the even function

Chapter 1, Problem 9

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Even Function and Odd Function Problem: Figure 1-6j shows the graph of the even function f(x) = x4 + 5x2 + Figure 1-6k shows the graph of the odd function g(x) = x3 + 6x. Figure 1-6j a. On the same screen, plot y1 = f(x) and y2 = f(x). Use thick style for y2. Based on the properties of negative numbers raised to even powers, explain why the two graphs are identical. b. Deactivate y1 and y2. On the same screen, plot y3 = g(x), y4 = g(x), and y5 = g(x). Use thick style for y5. Based on the properties of negative numbers raised to odd powers, explain why the graphs of y4 and y5 are identical. c. Even functions have the property f(x) = f(x). Odd functions have the property f( x) = f(x). Figure 1-6l shows two functions, h and j, but you dont know the equation of either function. Tell which function is an even function and which is an odd function. Figure 1-6l d. Let e(x) = 2x. Sketch the graph. Based on the graph, is function e an odd function, an even function, or neither? Confirm your answer algebraically by finding e(x). 1