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

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The graphs of ( f(x) = x^3 ) and ( g(x) = -(3x)^3 ) are related by a reflection about the y-axis and a horizontal compression by a factor of 1/3. This means that ( 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.

- How do you find the asymptotes for #f(x)=(5x^3-9x^2-6x-4)/(-6x^2-9x-7)#?
- How do you find the vertical, horizontal and slant asymptotes of: # f(x)=(2x - 2 )/( (x-1)(x^2 + x - 1))#?
- How do you determine whether # f(x) = (-x+1)(x+2)(x-3)^2# is an odd or even function?
- How do you find the domain of the following functions #f(x)= ln(x-x^2)#?
- If #f(x)= 1-x^3# and #g(x)= 1/x# how do you find f(g(x))?

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