Question

(07.06 MC) The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.

Answer 1

Answer:

2.

Step-by-step explanation:

We have been given the formula of a function $f(x)=2x+1$. We are asked to find the average rate of change of the given function between $x=0$ and $x=3$.

To find the average rate of change we will use formula:

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

Upon substituting our given values in above formula we will get,

$\text{Average rate of change}=\frac{f(3)-f(0)}{3-0}$

$\text{Average rate of change}=\frac{2\cdot 3+1-(2\cdot 0+1)}{3-0}$

$\text{Average rate of change}=\frac{6+1-(0+1)}{3}$

$\text{Average rate of change}=\frac{6}{3}$

$\text{Average rate of change}=2$

Therefore, the average rate of change for our given function between $x=0$ and $x=3$ is 2.

Answer 2

Find the rate of change at x=0 and at x=3, then find the average of those values.

f(0) = 2(0) + 1 = 1
f(3) - 2(3) + 1 = 7
 
$\frac{f(0)+f(3)}{2} = \frac{1 + 7}{2} = \frac{8}{2} = 4$

Answer: 4