1 Find the vertical asymptotes.Determine the horizontal asymptote.S(x) = 3r-1)(x+3)(x+2)(x-4)x+3r(x) =7-4x-12Find the y-intercept.Find the x- intercept(s).(x+1)(x-3)g(x) =(x+2)(x-2)(x+1)(x-5)g(x) =-(x+3)(x-3)3Find a polynomial of degree 3 with zeros 2 and 3i .4Find all rational, irrational, and complex zeros (ifapplicable):P(x) =x° +x² -5x² +x-6

Name: 1 Find the vertical asymptotes.Determine the horizontal asymptote.S(x)
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Description: 1 Find the vertical asymptotes.Determine the horizontal asymptote.S(x) = 3r-1)(x+3)(x+2)(x-4)x+3r(x) =7-4x-12Find the y-intercept.Find the x- intercept(s).(x+1)(x-3)g(x) =(x+2)(x-2)(x+1)(x-5)g(x) =-(x+3)(x-3)3Find a polynomial of degree 3 with zeros

1) The given function is rx=x+3x2-4x-12.

Answered: Find the vertical asymptotes. X+3 r(x)…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.CR: Chapter Review

Problem 13CC

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Question

Find the vertical asymptotes.
Determine the horizontal asymptote.
S(x) = 3r-1)(x+3)
(x+2)(x-4)
x+3
r(x) =
7-4x-12
Find the y-intercept.
Find the x- intercept(s).
(x+1)(x-3)
g(x) =
(x+2)(x-2)
(x+1)(x-5)
g(x) =-
(x+3)(x-3)
3
Find a polynomial of degree 3 with zeros 2 and 3i .
4
Find all rational, irrational, and complex zeros (if
applicable):
P(x) =x° +x² -5x² +x-6

Expert Solution

Step 1

The given function is $r (x) = \frac{x + 3}{x^{2} - 4 x - 12}$ .

Step 2

Rewrite the given function $r (x) = \frac{x + 3}{x^{2} - 4 x - 12}$ as shown below.

$\begin{array}{rcl} r (x) & = & \frac{x + 3}{x^{2} - 4 x - 12} \\ = & \frac{x + 3}{x^{2} - 6 x + 2 x - 12} \\ = & \frac{x + 3}{x (x - 6) + 2 (x - 6)} \\ = & \frac{x + 3}{(x - 6) (x + 2)} \end{array}$

Thus, $\begin{array}{rcl} r (x) & = & \frac{x + 3}{(x - 6) (x + 2)} \end{array}$ .

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