Question

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 3
0 0
1 -1

Match the average rates of change of f(x) to the corresponding intervals.

Tiles
-3
-8
-7
-4
Pairs
[-5, -1]

[-4, -1]

[-3, 1]

[-2, 1]

Answer 1

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

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

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 $\frac{f(-1)-f(-5)}{-1-(-5)}$.

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

Thus, we have $\frac{3-35}{-1+5} = \frac{-32}{4} =-8$


Part 2:

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

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

Thus, we have $\frac{3-24}{-1+4} = \frac{-21}{3} =-7$


Part 3:

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

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

Thus, we have $\frac{-1-15}{1+3} = \frac{-16}{4} =-4$


Part 4:

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

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

Thus, we have $\frac{-1-8}{1+2} = \frac{-9}{3} =-3$