Chapter 2: Q1. (page 65)

Explain Why $f (x) = \frac{x + 2}{2}$ is a linear function.

Short Answer

Expert verified

The given function $f (x) = \frac{x + 2}{2}$ is a linear function because it can be defined in the form of $f (x) = m x + b$ .

Step by step solution

– Definition of linear function.

A function $f (x)$ is a linear function if it can be defined as:

$f (x) = m x + b$

Where m,b are real numbers, m is the slope and b is the y-intercept of the function.

– Given information

The given function is:

$f (x) = \frac{x + 2}{2}$

– Explanation for the given problem.

The given function can be defined as:

$\begin{matrix} f (x) = \frac{x}{2} + \frac{2}{2} \\ f (x) = 0.5 x + 1 \end{matrix}$

The above function is in the form of $f (x) = m x + b$ , where m=0.5 and b=1.

Thus, the given function $f (x) = \frac{x + 2}{2}$ is a linear function because it can be defined in the form of $f (x) = m x + b$ .

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.

Explain Why $f (x) = \frac{x + 2}{2}$ is a linear function.

Short Answer

Step by step solution

– Definition of linear function.

– Given information

– Explanation for the given problem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Pure Maths

Probability and Statistics

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Explain Why fx=x+22 is a linear function.

Short Answer

Step by step solution

– Definition of linear function.

– Given information

– Explanation for the given problem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Pure Maths

Probability and Statistics

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Explain Why $f (x) = \frac{x + 2}{2}$ is a linear function.