Question

function $g(x)$

$x$	$-2$	$0$	$3$	$6$	$10$
$g(x)$	$-3$	$-7$	$-8$	$-3$	$13$

students starting expression: $\frac{-7 + (-3)}{2}$
click the arrows to choose an answer from each menu.
the expression to calculate the average rate of change over the interval $0,6$ is the
choose... . the average rate of change over the
specified interval is choose... . so, the students starting expression is choose... .

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $g(x)$ over interval $[a,b]$ is $\frac{g(b)-g(a)}{b-a}$.

Step2: Substitute $a=0, b=6$

From the table, $g(0)=-7$, $g(6)=-3$. Substitute values:
$\frac{g(6)-g(0)}{6-0}=\frac{-3-(-7)}{6-0}$

Step3: Calculate the value

Simplify numerator and denominator:
$\frac{-3+7}{6}=\frac{4}{6}=\frac{2}{3}$

Step4: Compare to student's expression

Student's expression is $\frac{-7+(-3)}{2}$, which does not match the correct formula, so it is incorrect.

Answer:

The expression to calculate the average rate of change over the interval $[0,6]$ is $\boldsymbol{\frac{-3-(-7)}{6-0}}$. The average rate of change over the specified interval is $\boldsymbol{\frac{2}{3}}$. So, the student's starting expression is $\boldsymbol{\text{incorrect}}$.