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Absolute Value Functions

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Absolute Value Functions

Study Guide

Key Definition

An absolute value function is a function that contains an algebraic expression within absolute value symbols. The absolute value parent function is defined as $f(x) = |x|$.

Important Notes

The graph of an absolute value function is V-shaped.
The vertex of the graph is at (0,0).
The domain is the set of all real numbers.
The range is the set of all real numbers greater than or equal to 0.
The x-intercept and the y-intercept are both 0 for the parent function.

Mathematical Notation

$|x|$ represents the absolute value of x.

The symbol |x| means the absolute value of x.

Why It Works

The absolute value of a number is its distance from 0 on the number line. So, the absolute value of both -x and x are the same.

Remember

Quick Reference

Absolute Value:$|x|$

Understanding Absolute Value Functions

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The absolute value of a number is its distance from zero on the number line. So, $|x|$ is always non-negative.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the absolute value of -3?

Real-World Problem

Question Exercise

Intermediate

Temperature Scenario

If the temperature dropped 5 degrees below zero, what is the absolute value of the temperature change?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $f(x) = |x + 2|$, what is the value of $f(-4)$?

Challenge Quiz

Single Choice Quiz

Advanced

If $f(x) = |x - 1| - 3$, what is the value of $f(2)$?

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