(Solved): 4b. Use the graph of f(x)=3x to obtain the graph of 4b. Use the graph of f shown below to obtain ...

4b. Use the graph of $$f(x)=\sqrt[3]{x}$$ to obtain the graph of 4b. Use the graph of $$f$$ shown below to obtain the graph $$h(x)=\sqrt[3]{?x}$$. of $$g(x)=f(?x)$$. The graph of $$h$$ is a reflection of the graph of $$f$$ about the $$y$$-axis because $$h(x)=f(?x)$$. Replace each $$x$$-coordinate with its opposite. Since the points $$(?1,?1),(0,0)$$, and $$(1,1)$$ are on the graph of $$f$$, the points $$(1,?1),(0,0)$$, and $$(?1,1)$$ are on the graph of $$h$$. Objective \#5: Use vertical stretching and shrinking to graph functions. Solved Problem \#5 Pencil Problem $$\#5$$ 5. Use the graph of $$f(x)=?x?$$ to obtain the graph of 5. Use the graph of $$f(x)=x^3$$ to obtain the graph of $$g(x)=2?x?$$. $$h(x)=\frac{1}{2}{x}^3$$. The graph of $$g$$ is obtained by vertically stretching the graph of $$f$$ because $$g(x)=2f(x)$$. Multiply each $$y$$-coordinate by 2 . Since the points $$(?2,2),(0,0)$$, and $$(2,2)$$ are on the graph of $$f$$, the points $$(?2,4),(0,0)$$, and $$(2,4)$$ are on the graph of $$g$$. Objective \#6: Use horizontal stretching and shrinking to graph functions. Solved Problem 46 Pencil Problem $$\#6$$. 2 we the gaph of $$f$$ shown below to graph each 6. Use the graph of $$f$$ shown below to graph cach function. 6a. $$g(x)=f(2x)$$ Divide the $$x$$-coordinate of each point on the graph of 6a. $$g(x)=f(2x)$$ $$f$$ by 2 . The points $$(?1,0),(0,3),(1,0),(2,?3)$$, and $$(3,0)$$ are on the graph of $$g$$. 6b. $$h(x)=f\left(\frac{1}{2}x\right)$$ 6b. $$g(x)=f\left(\frac{1}{2}x\right)$$ Multiply the $$x$$-coordinate of each point on the graph of $$f$$ by 2 . The points $$(?4,0),(0,3),(4,0),(8,?3)$$, and $$(12,0)$$ are on the graph of $$h$$.