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

Answer 1

Liam Brennan

#h(x)# is the standard function #f(x) =x^3# reflected about the #x-#axis and scaled by #1/3#

#h(x) =-1/3x^3#

Consider the "parent" function #f(x) =x^3# represented graphically below.

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

Then, #h(x) = -1/3xxf(x)# is represented graphically below.

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

Hence, we can observe that #h(x)# is the standard function #f(x) =x^3# rflected about the #x-#axis and scaled by #1/3#

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Answer 2

Elias Ackerman

The transformation of the function h(x) = -1/3x^3 involves a vertical compression by a factor of 1/3 compared to the parent function f(x) = x^3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.