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adell [148]
3 years ago
11

Compare the functions shown below in the attachment:

Mathematics
2 answers:
Ratling [72]3 years ago
8 0
I got 12.

f(x) = (x+3)^2 - 2 Plug in -1 for x to find the value. Plug in 3 for x to find that value.

For x = -1 I got the point (-1, 2). Let me check the second one reaFor x = 3, I got the point (3, 34). Now do I do the same thing I did before by subtracting the points, like in the formula you posted earlier

So the answer would be B,


aalyn [17]3 years ago
5 0
<h2>Answer:</h2>

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 is:

                         g(x) , f(x) , h(x)

 ( Since,

average rate of change of g(x) is:  1/2

average rate of change of f(x) is:  8

average rate of change of h(x) is:  12  )

<h2>Step-by-step explanation:</h2>

The average rate of a function from x=a to x=b is calculated by the formula:

\text{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}

Here a= -1 and b=3

a)

The function f(x) is given by:

f(x)=(x+3)^2-2

f(-1)=(-1+3)^2-2\\\\i.e.\\\\f(-1)=2^2-2\\\\i.e.\\\\f(-1)=4-2\\\\i.e.\\\\f(-1)=2

f(3)=(3+3)^2-2\\\\i.e.\\\\f(3)=6^2-2\\\\i.e.\\\\f(3)=36-2\\\\i.e.\\\\f(3)=34

Hence, the average rate of change of f(x) is:

\text{Average rate of change}=\dfrac{34-2}{3-(-1)}

i.e.

\text{Average rate of change}=\dfrac{32}{4}

i.e.

\text{Average rate of change}=8

b)

The function g(x) is a straight line that passes through:

(-1,-2) and (3,0)

i.e.

g(-1)= -2

g(3)=0

i.e. the average rate of change is given by:

\text{Average rate of change}=\dfrac{g(3)-g(-1)}{3-(-1)}

i.e.

\text{Average rate of change}=\dfrac{0-(-2)}{4}

i.e.

\text{Average rate of change}=\dfrac{2}{4}

i.e.

\text{Average rate of change}=\dfrac{1}{2}

c)

Based on the table of values we have:

h(-1)= 14

and

h(3)= 62

\text{Average rate of change}=\dfrac{h(3)-h(-1)}{3-(-1)}

i.e.

\text{Average rate of change}=\dfrac{62-14}{4}

i.e.

\text{Average rate of change}=\dfrac{48}{4}

i.e.

\text{Average rate of change}=12

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