Math  /  Algebra

QuestionPart 11 of 13 Points: 0 of 1 Save
Follow the steps for graphing a rational function to graph the function H(x)=4x2436x2H(x)=\frac{4 x-24}{36-x^{2}}. (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. It approaches \infty on one side of the asymptote(s) at x=6x=-6 and -\infty on the other. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) C. It approaches either \infty or -\infty on both sides of the asymptote(s) at x=x=\square. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) D. There is no vertical asymptote.
Determine the horizontal asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, y=0y=0. (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two horizontal asymptotes. The top asymptote is \square, and the bottom asymptote is \square \square (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no horizontal asymptote.
Determine the oblique asymptote(s), if any exist. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one oblique asymptote, \square (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two oblique asymptotes. The oblique asymptote with a negative slope is \square , and the oblique asymptote with a positive slope is \square . (Type equations. Use integers or fractions for any numbers in the equations.) C. There is no oblique asymptote.
Determine points, if any, at which the graph of H intersects the horizontal or oblique asymptote, if one exists. Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The graph of H intersects the horizontal or oblique asymptote at \square (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) B. The graph of H intersects the horizontal or oblique asymptote at infinitely many points. C. There is no point at which the graph of H intersects the horizontal or oblique asymptote. D. There is no horizontal or oblique asymptote.

Studdy Solution
Vertical asymptote: x=6x = -6, approaching \infty from the left and -\infty from the right. Horizontal asymptote: y=0y = 0. No intersection with the horizontal asymptote.
No oblique asymptote.

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord