Question

NO LINKS!!

Find the average rate of change of the function from x1 to x2.
function f(x) = -9x + 4
x-values x1 = -5, x2 = 0

Answer 1

-9

Explanation:

Given function:

`f(x)=-9x+4`

Given x-values:

• x₁ = -5
• x₂ = 0

Calculate the value of the function for the two given values of x:

`\begin{aligned}\implies f(x_1)&=-9(-5)+4\\&=45+4\\&=49\end{aligned}`

`\begin{aligned}\implies f(x_2)&=-9(0)+4\\&=0+4\\&=4\end{aligned}`

`\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$(f(b)-f(a))/(b-a)$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}`

As -5 < 0:

• a = x₁ = -5
• b = x₂ = 0

Therefore:

`\begin{aligned} \implies \textsf{Average rate of change}&=(f(x_2)-f(x_1))/(x_2-x_1)\\\\&=(4-49)/(0-(-5))\\\\&=(-45)/(5)\\\\&=-9\end{aligned}`