Question

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

Short answer

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

Step-by-step solution

– Definition of linear function.

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

$f\left(x\right)=mx+b$

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:

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

– Explanation for the given problem.

The given function can be defined as:

$\begin{array}{c}f\left(x\right)=\frac{x}{2}+\frac{2}{2}\\ f\left(x\right)=0.5x+1\end{array}$

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

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