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

The graph of

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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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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.

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.

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.

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- How do you find #f^-1(x)# given #f(x)=1/(x+2)#?
- Given #f(x) = 7x^2 - 5x#, #g(x) = 17x - 4# how do you find (fog)(6)?
- How do you identify the oblique asymptote of #f(x) = (2x^2+3x+8)/(x+3)#?
- How do you find the vertical, horizontal or slant asymptotes for #y=(2x^2-3x+4)/(x+2)#?

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