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?

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)