Consider the function f(x) For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts. a. Determine the vertical intercept of f. f(0) = 7/48 b. Determine the zeros (or "roots") of f. x = -sqrt(7), sqrt(7) x² 7 (4x12)(x + 4) X= -4 Preview c. Determine the vertical asymptote(s) of f. y = Preview Preview d. Determine the horizontal asymptote of f. Preview 7 48 = 0.14583333333333334. √7 -2.6457513110645907., √7 -4 -4. 2.6457513110645907.
Consider the function f(x) For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts. a. Determine the vertical intercept of f. f(0) = 7/48 b. Determine the zeros (or "roots") of f. x = -sqrt(7), sqrt(7) x² 7 (4x12)(x + 4) X= -4 Preview c. Determine the vertical asymptote(s) of f. y = Preview Preview d. Determine the horizontal asymptote of f. Preview 7 48 = 0.14583333333333334. √7 -2.6457513110645907., √7 -4 -4. 2.6457513110645907.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Consider the function f(x)=x2−7(4x−12)(x+4). For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts.
(D)
![**Consider the function** \( f(x) = \frac{x^2 - 7}{(4x - 12)(x + 4)} \).
*For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts.*
### a. Determine the vertical intercept of \( f \).
\[
f(0) = \frac{7}{48} \quad \text{Preview} \quad \frac{7}{48} = 0.14583333333333334
\]
### b. Determine the zeros (or "roots") of \( f \).
\[
x = -\sqrt{7}, \sqrt{7} \quad \text{Preview} \quad -\sqrt{7} = -2.6457513110645907 , \quad \sqrt{7} = 2.6457513110645907
\]
### c. Determine the vertical asymptote(s) of \( f \).
\[
x = -4 \quad \text{Preview} \quad -4 = -4
\]
### d. Determine the horizontal asymptote of \( f \).
\[
y = 0 \quad \text{Preview}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a31831f-6f00-4468-acbe-9e4738be30a7%2F71bc63b8-cd88-4e98-a723-439592a3dc99%2Fzhqalp_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the function** \( f(x) = \frac{x^2 - 7}{(4x - 12)(x + 4)} \).
*For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts.*
### a. Determine the vertical intercept of \( f \).
\[
f(0) = \frac{7}{48} \quad \text{Preview} \quad \frac{7}{48} = 0.14583333333333334
\]
### b. Determine the zeros (or "roots") of \( f \).
\[
x = -\sqrt{7}, \sqrt{7} \quad \text{Preview} \quad -\sqrt{7} = -2.6457513110645907 , \quad \sqrt{7} = 2.6457513110645907
\]
### c. Determine the vertical asymptote(s) of \( f \).
\[
x = -4 \quad \text{Preview} \quad -4 = -4
\]
### d. Determine the horizontal asymptote of \( f \).
\[
y = 0 \quad \text{Preview}
\]
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