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How are the graphs #f(x)=x^3# and #g(x)=-(2x)^3# related?

Answer 1

The graph of #g(x)# can be described as a transformation of the graph of #f(x)#.

First, take a look at the graph of #f(x)#. graph{x^3 [-10, 10, -5, 5]}

Now look at the graph of #g(x)#. graph{-(2x)^3 [-10, 10, -5, 5]}

The graph of #f(x)# is horizontally shrunk by a factor of #1/2# and reflected over the #y#-axis to get the graph of #g(x)#.

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Answer 2

Ariana Alvarez

The graphs of ( f(x) = x^3 ) and ( g(x) = -(2x)^3 ) are related as follows:

Both functions represent cubic polynomials.
The function ( g(x) = -(2x)^3 ) is obtained by applying a horizontal compression and a reflection across the x-axis to the graph of ( f(x) = x^3 ).
Specifically, the factor of 2 inside the parentheses in ( g(x) ) compresses the graph horizontally by a factor of 2, and the negative sign outside the parentheses reflects the graph across the x-axis.
Therefore, ( g(x) ) is a horizontally compressed and reflected version of ( f(x) ).

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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.