#14 c. (1-V-1)(1+ V-1)12. Find all the real zeros and state their multiplicities of 2a+5x2 -13. Combine the following into a single logarithm1In x-3 In (2 + 4) +In (y))Find all the intercepts and asymptotes of the following rational functions, then graph it.r2 - 914.r (x) =2x2 +1PrtScnHomeEndF4F5F6F7F8F9

Name: #14 c. (1-V-1)(1+ V-1)12. Find all the real zeros and state their mult
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Description: #14 c. (1-V-1)(1+ V-1)12. Find all the real zeros and state their multiplicities of 2a+5x2 -13. Combine the following into a single logarithm1In x-3 In (2 + 4) +In (y))Find all the intercepts and asymptotes of the following rational functions, then g

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Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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#14

c. (1-V-1)(1+ V-1)
12. Find all the real zeros and state their multiplicities of 2a+5x2 -
13. Combine the following into a single logarithm
1
In x
-3 In (2 + 4) +In (y))
Find all the intercepts and asymptotes of the following rational functions, then graph it.
r2 - 9
14.
r (x) =
2x2 +1
PrtScn
Home
End
F4
F5
F6
F7
F8
F9

Expert Solution

Step 1

Given , y= $r (x) = \frac{x^{2} - 9}{2 x^{2} + 1}$

we have to find the all intercepts and asymptotes of the rational function

Step 2

$A) f i r s t l y w e h a v e t o f i n d a l l i n t e r c e p t s T o f i n d x - i n t e r c e p t, p l u g i n y = 0 0 = y = \frac{x^{2} - 9}{2 x^{2} + 1} s o, c r o s s m u l t i p l y e a c h o t h e r w e g e t, x^{2} - 9 = 0 \Rightarrow x^{2} - 3^{2} = 0 \Rightarrow (x + 3) (x - 3) = 0 \Rightarrow x + 3 = 0 a n d x - 3 = 0 \Rightarrow x = 3 a n d - 3 t h e r e f o r e x - i n t e r c e p t s a r e (3, 0) a n d (- 3, 0) N o w, T o f i n d y - i n t e r c e p t, p l u g i n x = 0 \Rightarrow y = \frac{{(0)}^{2} - 9}{2 {(0)}^{2} + 1} = \frac{- 9}{1} = - 9 t h e r e f o r e y - i n t e r c e p t s i s (0, - 9)$

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