Answer:
Δy = -8
Δx = 5
Average rate of change = -8/5
Explanation:
Given:
The graph of y = f(x)
To find:
The average rate of change oer the interval− 2≤x≤3
[tex]\begin{gathered} Average\text{ rate of change is given as: }\frac{f(b\text{ - a\rparen}}{b\text{ - a}} \\ where\text{ a\le x\le b is the interval} \\ −2≤x≤3:\text{ a =-2, b = 2} \\ \\ Based\text{ on the formula we are given in the question:} \\ Average\text{ rate of change = }\frac{\Delta y}{\Delta x} \end{gathered}[/tex]
When x = -2
f(x) = 8
when x = 3
f(x) = 0
We will connect the vlus of both f(x)with a line
[tex]\begin{gathered} \Delta y\text{ = 0 - 8} \\ \Delta y\text{ =-8} \\ \Delta\text{x = 3 - \lparen-2\rparen} \\ \Delta\text{x = 3 + 2 = 5} \\ \\ Average\text{ rate of change = }\frac{0\text{ - 8}}{3-(-2)} \\ Average\text{ rate of change = }\frac{0-8}{3+2} \end{gathered}[/tex][tex]Average\text{ rate of change = }\frac{-8}{5}[/tex]
