Instructions:Drag each tile to the correct box.The function f(x) is represented by this table of values.x f(x)-5 35-4 24-3 15-2 8-1 30 01 -1Match the average rates of change of f(x) to the corresponding intervals.Tiles-3-8-7-4Pairs[-5, -1][-4, -1][-3, 1][-2, 1]

The average rate of change of a function, f(x), over a given interval [a, b] is given by:

Average rate of change = [tex] \frac{f(b)-f(a)}{b-a} [/tex]

Given a table of value for the function f(x) for given x values.

Part 1:

The average rate of change of f(x) over the interval [-5, -1] is given by [tex] \frac{f(-1)-f(-5)}{-1-(-5)}[/tex].

From the given table, f(-1) = 3 and f(-5) = 35.

Thus, we have [tex] \frac{3-35}{-1+5} = \frac{-32}{4} =-8[/tex]


Part 2:

The average rate of change of f(x) over the interval [-4, -1] is given by [tex] \frac{f(-1)-f(-4)}{-1-(-4)}[/tex].

From the given table, f(-1) = 3 and f(-4) = 24.

Thus, we have [tex] \frac{3-24}{-1+4} = \frac{-21}{3} =-7[/tex]


Part 3:

The average rate of change of f(x) over the interval [-3, 1] is given by [tex] \frac{f(1)-f(-3)}{1-(-3)}[/tex].

From the given table, f(1) = -1 and f(-3) = 15.

Thus, we have [tex] \frac{-1-15}{1+3} = \frac{-16}{4} =-4[/tex]


Part 4:

The average rate of change of f(x) over the interval [-2, 1] is given by [tex] \frac{f(1)-f(-2)}{1-(-2)}[/tex].

From the given table, f(1) = -1 and f(-2) = 8.

Thus, we have [tex] \frac{-1-8}{1+2} = \frac{-9}{3} =-3[/tex]