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]

Interval          rate of change
[-5, -1]                 -8

[-4, -1]                 -7

[-3, 1]                  -4

[-2, 1]                  -3


Explanation:


1) Table

x      f(x)

-5     35

-4     24

-3     15

-2       8

-1       3

  0      0

 1       -1


2) Solution:

i) formula: rate of change = [change in f(x)] / [change in x]

ii) interval [-5, -1] ⇒ 

rate of change = [ f(1) - f(-5) ] / [-1 - (-5)] = [-1 - 35] / [-1+5] = -36 / 4 = - 8

iii) interval [-4, -1] ⇒ 

rate of change = [ f(-1) - f(-4) ] / [ -1 - (-4) ] = [3 - 24] / [-1 + 4] = -21/3 = - 7

iv) interval [-3,1] ⇒

rate of change = [ f(1) - f(-3) ] / [ 1 - (-3) ] = [-1 - 15] / [1 + 3] = -16/4 = - 4

v) interval [-2,1] ⇒

rate of change = [f (1) - f(-2)] / [1 - (-2)] = [ -1 - 8] / [1 + 2] = -9/3 = -3