Chapter 4: Q. 54 (page 274)

Graph each function. State the domain and range.
$f (x) = | 2 x - 2 |$

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. Solve for x.

Since $f (x)$ cannot be negative , so the minimum point of the graph will be where

$f (x) = 0$

$\begin{matrix} f (x) = | 2 x - 2 | \\ f (x) = \pm (2 x - 2) = 0 \\ 2 x - 2 = 0 \\ 2 x = 2 \\ x = 1 \end{matrix}$

f(x)Step 3. Make a table for the given function.

Construct a table for by taking some values ofx.

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.

Years Since 2000	0	1	2	3	4
Number of children	4269	4279	4939	5209	6936

Days Since Movie Opened	1	2	3	4	5	6	7
Daily Ticket Sales ( $$$ )	85	92	89	78	65	68	55

Graph each function. State the domain and range.
$f (x) = | 2 x - 2 |$

Short Answer

Step by step solution

Step 1. State the concept for absolute value function.

Step 2. Solve for x.

f(x)Step 3. Make a table for the given function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Applied Mathematics

Decision Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Graph each function. State the domain and range.f(x)=|2x−2|

Short Answer

Step by step solution

Step 1. State the concept for absolute value function.

Step 2. Solve for x.

f(x)Step 3. Make a table for the given function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Applied Mathematics

Decision Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Graph each function. State the domain and range.
$f (x) = | 2 x - 2 |$