Consider the following.3x + 8C(x) = 2*x + 3(a) State the domain of the function.O all real numbers xO all real numbers x except x = -3O all real numbers x except x = 8O all real numbers x except x = -8O 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.y15r1510105-15- 1051015-15-10-51015-5-5--1010-1515y1515101055-15-10-51015- 15-10-51015-5-510-10-15-15

Hence, the correct Answer is all real numbers x, except x=-3 (Second Option)

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.)

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

Problem 1RQ

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

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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