91Ó°ÊÓ

Given that the linear function is$f\left(x\right)=2x+3.$

Here, the linear function is$f\left(x\right)=2x+3.$We know that in a linear function $y=mx+b$, $m$is the slope and $b,$is y- intercept.

So, in the given function slope is $2$and y- intercept$3.$

The graph of given function is

Linear functions have a constant average rate of change. That is, the average rate of change of a linear function $f\left(x\right)=mx+b$is $\frac{∆y}{∆x}=m.$

So, in the given linear function$f\left(x\right)=2x+3$the average rate of change is$2.$

Since, we know that the linear function $f\left(x\right)=mx+b$is increasing over its domain if its slope $m$, is positive. It is decreasing over its domain if its slope $m$, is negative. It is constant over its domain if its slope, $m$, is zero.

Here, in given linear function $f\left(x\right)=2x+3$, slope is positive so linear function is increasing.