Question

Compare the functions shown below: f(x) = (x + 3)2 − 2 g(x) linear graph with y intercept of negative 3 over 2 and x intercept of 3 h(x) x y −3 2 −2 7 −1 14 0 23 1 34 2 47 3 62 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3?

Answer 1

By definition we have the average rate of change is:
 AVR = (f (x2) -f (x1)) / ((x2) - (x1))
 Then, for each function we have:

 For f (x):
 f (x) = (x + 3) ^ 2 - 2
 For x = -1
 f (-1) = (-1 + 3) ^ 2 - 2
 f (-1) = (2) ^ 2 - 2
 f (-1) = 4 - 2
 f (-1) = 2
 For x = 3
 f (3) = (3 + 3) ^ 2 - 2
 f (3) = (6) ^ 2 - 2
 f (3) = 36 - 2
 f (3) = 34
 AVR = ((34) - (2)) / ((3) - (- 1))
 AVR = 8

 For g (x):
 linear graph with and intercept of negative 3 over 2 and x intercept of 3
 y = mx + b
 b = -3/2
 For me we have:
 0 = m (3) - 3/2
 3m = 3/2
 m = 1/2
 The function g (x) is:
 g (x) = (1/2) x - 3/2
 For x = -1
 g (-1) = (1/2) (- 1) - 3/2
 g (-1) = -1/2 - 3/2
 g (-1) = -4/2
 g (-1) = -2
 For x = 3
 g (3) = (1/2) (3) - 3/2
 g (3) = 3/2 - 3/2
 g (3) = 0
 AVR = ((0) - (- 2)) / ((3) - (- 1))
 AVR = 1/2

 For h (x):
 Using the table we have:
 AVR = ((62) - (14)) / ((3) - (- 1))
 AVR = 12

 from least to greatest:
 1) g (x)
 2) f (x)
 3) h (x)

 Answer:
 The correct order of the functions from least to greatest is:
 1) g (x)
 2) f (x)
 3) h (x)