Questions: Select the correct answer from each drop-down menu. The parent function f(x)=x^3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C. Graph B represents the function g(x)= Graph C represents the function h(x)=

Select the correct answer from each drop-down menu. The parent function f(x)=x^3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C. Graph B represents the function g(x)= Graph C represents the function h(x)=
Transcript text: Select the correct answer from each drop-down menu. The parent function $f(x)=x^{3}$ is represented by graph A Graph A is transformed to get graph B and graph C. Write the functions represented by graph $B$ and graph $C$. Graph B represents the function $g(x)=$ $\square$ Graph C represents the function $h(x)=$ $\square$
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Solution

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Solution Steps

Step 1: Identify the Parent Function

The parent function given is \( f(x) = x^3 \), represented by graph A.

Step 2: Analyze Graph B

Graph B is a vertical stretch of the parent function. The graph is stretched by a factor of 2, so the function for graph B is \( g(x) = 2x^3 \).

Step 3: Analyze Graph C

Graph C is a horizontal shift of the parent function. The graph is shifted to the right by 1 unit, so the function for graph C is \( h(x) = (x-1)^3 \).

Final Answer

  • Graph B represents the function \( g(x) = 2x^3 \).
  • Graph C represents the function \( h(x) = (x-1)^3 \).
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