Question

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 given data is shown in the table below.

x:      -5    -4    -3    -2     -1    0    1
f(x):  35   24    15     8     3    0   -1

A graph of the data is shown below.

Calculate rates of change, r.
Interval: [-5, -1]
r = (35 - 3)/(-5+1) = -8   (tile -8)

Interval: [-4, -1]:
r = (24 - 3)/(-4 + 1) = -7   (tile -7)

Interval: [-3, 1]:
r = (15 + 1)/(-3 - 1) = -4    (tile - 4)

Interval: [-2, 1]
r = (8 + 1)/(-2 - 1) = -3     (tile -3)

Answer:

Tile   Interval
-----    ----------
  -3     [-2, 1]
  -4     [-3, 1]
  -7     [-4, -1]
  -8     [-5, -1]