Chapter 4: Q53. (page 274)

Graph each function. State the domain and range.
$f (x) = | x |$

Short Answer

Expert verified

The domain is all real numbers and the range is non-negative real numbers i.e.,

${y : y \geq 0}$

Step by step solution

Step 1. State the concept for absolute value function.

An absolute value function is a function that contains an algebraic expression within absolute value symbols. The absolute value of a number is its distance from 0 on the number line.

$f (x) = | x | = {\begin{matrix} x; x > 0 \\ - x; x \leq 0 \end{matrix}}$

Step 2. Make a table for the given function.

Construct a table for $f (x) = | x |$ by taking some values of $x$ .

$x$	$y = f (x) = \| x \|$
$- 2$	2
$- 1$	1
0	0
1	1
2	2

Step 3. Plot the graph.

Plot the values of $x$ and $f (x)$ on a graph,

The $x$ -coordinate values specify the domain of the function. Since the graph covers all possible values of $x$ , the domain is all real numbers.

The $y$ -coordinate values specify the range of the function. Since, the graph does not take any value less than or any negative value, the range is .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Graph each function. State the domain and range.
$f (x) = | x |$

Short Answer

Step by step solution

Step 1. State the concept for absolute value function.

Step 2. Make a table for the given function.

Step 3. Plot the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Graph each function. State the domain and range.f(x)=|x|

Short Answer

Step by step solution

Step 1. State the concept for absolute value function.

Step 2. Make a table for the given function.

Step 3. Plot the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Graph each function. State the domain and range.
$f (x) = | x |$