Question

7
given the functions f(x) and h(x) shown below. list the functions from greatest to least by average rate of change over the interval $0 \leq x \leq 3$. (a.fgr.9.5)

$x$	0	1	2	3

a not enough information
b f(x), h(x)
c same rate of change

Explanation:

Step1: Find avg rate of f(x)

The average rate of change formula is $\frac{f(x_2)-f(x_1)}{x_2-x_1}$. For $f(x)$, $x_1=0, f(x_1)=1$; $x_2=3, f(x_2)=7$.
$\text{Rate}_f = \frac{7-1}{3-0} = \frac{6}{3} = 2$

Step2: Find avg rate of h(x)

From the graph, $x_1=0, h(x_1)=2$; $x_2=3, h(x_2)=0$.
$\text{Rate}_h = \frac{0-2}{3-0} = \frac{-2}{3} \approx -0.67$

Step3: Compare the two rates

$2 > -0.67$, so $f(x)$ has a greater average rate of change than $h(x)$.

Answer:

B. f(x), h(x)