Question

For the following exercises, find the average rate of change of the functions from x = 1 to x =2.

Answer 1

Answer:

For the function $f(x)=4 x-3$ the average rate change from x is equal 1 to x is equal 2 is 4 .

Step-by-step explanation:

A function is given f(x)=4x-3.

It is required to find the average rate change of the function from x is 1 to x is 2 . simplify.

Step 1 of 2

A function f(x)=4 x-3 is given.

Determine the function $f\left(x_{1}\right)$ by putting the value of x=1 in the given function.

$\begin{aligned}&f(1)=4(1)-3 \\&f(1)=1\end{aligned} f(1)=1$

Determine the function $f\left(x_{1}\right)$ by putting the value of x is 2 in the given function.

$\begin{aligned}&f(2)=4(2)-3 \\&f(2)=5\end{aligned}$

Step 2 of 2

According to the formula of average rate change of the equation $\frac{\Delta y}{\Delta x}=\frac{f\left(x_{2}\right)-f\left(x_{2}\right)}{x_{2}-x_{1}}$

Substitute the value of $f\left(x_{1}\right)$ with, $f\left(x_{1}\right)$ with $3, x_{2}$ with 2 and $x_{1}$ with 1 .

$\begin{aligned}&\frac{\Delta y}{\Delta x}=\frac{5-1}{1} \\&\frac{\Delta y}{\Delta x}=4\end{aligned}$