Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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.](https://content.bartleby.com/qna-images/question/392e3fb2-e478-4be4-a49a-a76e7431547f/8f6a628a-16a6-4cea-ba3d-8cedabf35273/k94f23g.jpeg)
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
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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.
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