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Asymptotes

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1. f(x) = x^3 + x^2 - 4x - 4.

(a) What is the end behavior of this function? (Does it go up or down to the left? Does it go up or down the right?)
(b) What is the maximum number of turning points for this function?

2. Give the coordinates of the vertex of the parabola y = (x + 2)^2 + 5.

3. Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the function f(x) = -2x^3 + x^2 - x + 7.

4. f(x) = (3x^2) / (x^2 - 4)

(a) Give the domain of this function.
(b) Give any horizontal asymptotes.
(c) Give any vertical asymptotes.

5. If y varies directly as x, and y = 36 when x = 12, write an equation for y in terms of x.

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The solution describes Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for a function f(x) and the determination of horizontal and vertical asymptotes of a function.

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