(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

6. Draw a graph of the function f, and determine the intervals on which f is increasing and on which f is decreasing where f(x)=2x^{3}-3x^{2}-12x

9. Suppose the graph of f is given. Using transformations, describe how the graph of the following function can be obtained from the graph of f: y=2f(x+4)-5

21. Find the equation of the horizontal asymptote of the function g(x)=[tex]\frac{x^{3}}{3x^{3}-2x}[/tex].

2. Relevant equations

6. f(x)=2x^{3}-3x^{2}-12x

9. y=2f(x+4)-5

21. g(x)=[tex]\frac{x^{3}}{3x^{3}-2x}[/tex]

3. The attempt at a solution

6. Calculated graph in which local maximum was (-1,7) and local minimum was (2,-20). Said that for -[tex]\infty[/tex] through -1, y is increasing and for -1 through 2, y is decreasing, and for 2 through [tex]\infty[/tex], y is increasing.

9. (x+4) means left 4, -5 means down 5, 2 means twice the height, - means reflect over x-axis.

21. g(x)=[tex]\frac{x^{2}}{3x^{2-}2}[/tex] so the horizontal asymptote must equal 0 because the lim g(x) as x[tex]\rightarrow\infty[/tex]=0.

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# Homework Help: Various Problems for Precalculus Exam, Unit 1

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