Consider the following. 3x + 8 C(x) = x +3 (a) State the domain of the function. O all real numbers x all real numbers x except x = -3 all real numbers x except x = 8 all real numbers x except x = -8 O all real numbers x except x = 3 (b) Identify all intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) = y-intercept (x, y) = (c) Find any vertical and horizontal asymptotes. (Enter your answers as a comma-separated list of equations. If there are no asymptotes, enter DNE.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following.
3x + 8
C(x) = 2*
x + 3
(a) State the domain of the function.
O all real numbers x
O all real numbers x except x = -3
O all real numbers x except x = 8
O all real numbers x except x = -8
O all real numbers x except x = 3
(b) Identify all intercepts. (If an answer does not exist, enter DNE.)
x-intercept
(x, y) = (
y-intercept
(x, v) = (|
(c) Find any vertical and horizontal asymptotes. (Enter your answers as a comma-separated list of equations. If there are no asymptotes, enter DNE.)
(d) Plot additional solution points as needed to sketch the graph of the rational function.
y
15r
15
10
10
5
-15
- 10
5
10
15
-15
-10
-5
10
15
-5
-5-
-10
10
-15
15
y
15
15
10
10
5
5
-15
-10
-5
10
15
- 15
-10
-5
10
15
-5
-5
10
-10
-15
-15
Transcribed Image Text:Consider the following. 3x + 8 C(x) = 2* x + 3 (a) State the domain of the function. O all real numbers x O all real numbers x except x = -3 O all real numbers x except x = 8 O all real numbers x except x = -8 O all real numbers x except x = 3 (b) Identify all intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) = ( y-intercept (x, v) = (| (c) Find any vertical and horizontal asymptotes. (Enter your answers as a comma-separated list of equations. If there are no asymptotes, enter DNE.) (d) Plot additional solution points as needed to sketch the graph of the rational function. y 15r 15 10 10 5 -15 - 10 5 10 15 -15 -10 -5 10 15 -5 -5- -10 10 -15 15 y 15 15 10 10 5 5 -15 -10 -5 10 15 - 15 -10 -5 10 15 -5 -5 10 -10 -15 -15
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