Math  /  Algebra

QuestionPart 4 of 8 a. Find the slant asymptote of the graph of the rational function. b. Follow the seven-step strategy and use the slant asymptote to graph the rational function. f(x)=x3+64x2+5xf(x)=\frac{x^{3}+64}{x^{2}+5 x} b. To graph the function, first determine the symmetry of the graph of ff. Choose the correct answer be y -axis symmetry neither yy-axis symmetry nor origin symmetry origin symmetry What is the yy-intercept? Select the correct choice below and, if necessary, fill in the answer box to com A. The yy-intercept is \square (Type an integer or a simplified fraction.) B. There is no yy-intercept.
What is/are the xx-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box A. The xx-intercept(s) is/are \square 7. (Type an integer or a simplified fraction. Use a comma to separate answers if needed.) B. There are no x -intercepts.

Studdy Solution
Solve x3+64=0 x^3 + 64 = 0 to find x=4 x = -4 . Thus, the x x -intercept is (4,0)(-4, 0).
The slant asymptote is y=x5 y = x - 5 . The function has neither y y -axis symmetry nor origin symmetry. There is no y y -intercept. The x x -intercept is (4,0)(-4, 0).

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