Question

For the polynomial function f(x) = −5x(x + 2)2(x − 1)3:

For the polynomial function f(x) = -5x(x + 2)(x - 1)": 7. (4 points) The leading term when expanded is -5.2". Use this to describe the end be havior of f(x): as r → , f(x) → as I + -00, f(x) → 8. (4 points) Name the zeros of f(x) and each of their multiplicities. 9. (4 points) Come up with a rational function which has y = -5 as a horizontal asymptote.

Answer 1

7.

so,

$x\rightarrow \infty , f(x)\rightarrow -\infty$

$x\rightarrow -\infty , f(x)\rightarrow -\infty$

8.

zero	0	-2	1
multiplicity	1	2	3

9.

for horizontal asymptote to be y = -5 .

$lim_{x\rightarrow \infty }y = -5$

so,

$y = \frac{-5x}{x-2}$