Absolute Value Functions - Varsity Tutors

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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

concept. Use space or enter to play video.concept thumbnailBeginner

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Beginner Explanation

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

Practice Problems

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1

Quick Quiz

Single Choice QuizBeginner

What is the absolute value of -3?

A$-3$B$3$C$0$D$-1$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Temperature Scenario

If the temperature dropped 5 degrees below zero, what is the absolute value of the temperature change?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

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

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

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

A$-2$B$-1$C$0$D$1$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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