Question

pass the problem: partner b
directions: start by answering the question in your letter box below. then pass the paper around the circle until all parts of the question have been answered.
a function is given by:
f(x) = 3\sqrt{x + 2} - 3
partner b:
find the average rate of change on the interval 2,7.
\frac{y^{2}-y}{x_{2}-x_{1}}=
now pass the paper to partner c.
partner c:
check the work of partner b and make any corrections if necessary. describe the end behavior of the function.
as x→____, f(x)→____
as x→____, f(x)→____
now pass the paper to partner a.

Explanation:

Step1: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x)=3\sqrt{x + 2}-3 \).

$$
LATEXBLOCK0
$$

Step2: Calculate \( f(7) \)

Substitute \( x = 7 \) into \( f(x)=3\sqrt{x + 2}-3 \).

$$
LATEXBLOCK1
$$

Step3: Use the average rate of change formula \( \frac{f(x_2)-f(x_1)}{x_2 - x_1} \)

Here \( x_1 = 2,f(x_1)=3,x_2 = 7,f(x_2)=6 \)

$$ \frac{f(7)-f(2)}{7 - 2}=\frac{6 - 3}{5}=\frac{3}{5}=0.6 $$

Answer:

The average rate of change on the interval \([2,7]\) is \(0.6\)