Ask Question
10 December, 13:10

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?

+5
Answers (1)
  1. 10 December, 16:01
    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)
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers