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...
Related questions
Question
Is |3x-1| a function?
![The image contains a portion of a math problem and its solution explaining a function evaluation.
### Function Evaluation
#### Problem:
Evaluate the function \( f(x) \) at \( x = -5 \).
#### Solution:
\[
c) \quad f(-5) =
\]
Calculating:
\[
f(-5) = (-5)^2 - 2
\]
\[
f(-5) = 25 - 2
\]
\[
f(-5) = 23
\]
The solution shows step-by-step how to substitute \( x = -5 \) into the function \( f(x) = x^2 - 2 \) and calculate the result, which is 23.
Note: There is also a part of another equation visible at the bottom starting with:
\[
c) \quad y = |3x - 1|
\]
However, it is partially obscured, and no further information is available from the visible section.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F392e3fb2-e478-4be4-a49a-a76e7431547f%2F8f6a628a-16a6-4cea-ba3d-8cedabf35273%2Fk94f23g.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a portion of a math problem and its solution explaining a function evaluation.
### Function Evaluation
#### Problem:
Evaluate the function \( f(x) \) at \( x = -5 \).
#### Solution:
\[
c) \quad f(-5) =
\]
Calculating:
\[
f(-5) = (-5)^2 - 2
\]
\[
f(-5) = 25 - 2
\]
\[
f(-5) = 23
\]
The solution shows step-by-step how to substitute \( x = -5 \) into the function \( f(x) = x^2 - 2 \) and calculate the result, which is 23.
Note: There is also a part of another equation visible at the bottom starting with:
\[
c) \quad y = |3x - 1|
\]
However, it is partially obscured, and no further information is available from the visible section.
Expert Solution

Step 1
A relation is said to be a function only when every point in the domain has a unique value in the range.
if f(x) is a function then for x is equal to any value there must be a unique f(x) . If any of the point in the domain will give more than one range then the relation will not be a function.
To check whether the given relation is a function or not we can use vertical line test. Draw the graph of the given relation, if a vertical line crosses the relation on the graph only once in all location then the relation is a function.
Step by step
Solved in 4 steps with 2 images

Recommended textbooks for you

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning