How do you identify the transformation of h(x)=-1/3x^3?

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Alan N. Share
Feb 20, 2018

Answer:

$h \left(x\right)$ is the standard function $f \left(x\right) = {x}^{3}$ reflected about the $x -$axis and scaled by $\frac{1}{3}$

Explanation:

$h \left(x\right) = - \frac{1}{3} {x}^{3}$

Consider the "parent" function $f \left(x\right) = {x}^{3}$ represented graphically below.

graph{x^3 [-10, 10, -5, 5]}

Then, $h \left(x\right) = - \frac{1}{3} \times f \left(x\right)$ is represented graphically below.

graph{-1/3x^3 [-10, 10, -5, 5]}

Hence, we can observe that $h \left(x\right)$ is the standard function $f \left(x\right) = {x}^{3}$ rflected about the $x -$axis and scaled by $\frac{1}{3}$

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