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.

Answered: Is |3x-1| a function?

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

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.

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.