place (click and drag) the functions below in order from smallest to largest average rate of change over the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$ and $b = 8$.

Step2: Calculate average rate of change for $f(x)=2x + 20$

$f(8)=2\times8 + 20=16 + 20=36$, $f(2)=2\times2+20=4 + 20 = 24$. Then $\frac{f(8)-f(2)}{8 - 2}=\frac{36 - 24}{6}=\frac{12}{6}=2$.

Step3: Calculate average rate of change for $g(x)=x^{2}-3x + 18$

$g(8)=8^{2}-3\times8 + 18=64-24 + 18=58$, $g(2)=2^{2}-3\times2 + 18=4-6 + 18=16$. Then $\frac{g(8)-g(2)}{8 - 2}=\frac{58 - 16}{6}=\frac{42}{6}=7$.

Step4: Calculate average rate of change for $h(x)=1.2^{x}$

$h(8)=1.2^{8}\approx4.299817$, $h(2)=1.2^{2}=1.44$. Then $\frac{h(8)-h(2)}{8 - 2}=\frac{4.299817-1.44}{6}=\frac{2.859817}{6}\approx0.476636$.

Answer:

Least: $h(x)=1.2^{x}$, Middle: $f(x)=2x + 20$, Greatest: $g(x)=x^{2}-3x + 18$