Math  /  Algebra

Questionstion list Iestion y estion 10 estion 11 estion 12 stion 13 stion 14 stion 15 tion 16 ion 17 ion 18 on 19 on 20 B. The function has two vertical asymptotes. The leftmost asymptote is , and the rightmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) C. The function has three vertical asymptotes. The leftmost asymptote is \square, the middle asymptote is (Type equations. Use integers or fractions for any numbers in the equations.) D. There is no vertical asymptote.
Determine the hole, if it exists. Select the correct choice and, if necessary, fill in the answer box to complete your choice. There is a hole in the graph at the point (6,13)\left(6,-\frac{1}{3}\right). (Type an ordered pair using integers or simplified fractions.) B. There are no holes in the graph.
Determine the behavior of the graph on either side of any vertical asymptotes, if any exist. Select the correct choice and, if necessary, fill in any answer box(es) to complete your choice. A. It approaches \infty on one side of the asymptote(s) at x=\mathrm{x}=\square and -\infty on the other. It approaches either \infty or -\infty on both sides of the asymptote(s) at x=\mathrm{x}= \square \square \square . Save Points: 0 of 1
Follow the steps for graphing a rational function to graph the function H(x)=4x2436x2H(x)=\frac{4 x-24}{36-x^{2}}. and the rightmost asymptote is \square

Studdy Solution
The function simplifies to H(x)=4x+6H(x) = \frac{-4}{x + 6}.
There is a hole at (6,13)(6, -\frac{1}{3}).
There is a vertical asymptote at x=6x = -6.
The function approaches \infty as xx approaches 6-6 from the left, and approaches -\infty as xx approaches 6-6 from the right.

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