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3 August, 02:36

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?

+3
Answers (1)
  1. 3 August, 02:51
    0
    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)
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