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ryzh [129]
3 years ago
7

Which of the given functions have an average rate of change of -12 on the interval [0, 2]?

Mathematics
2 answers:
klemol [59]3 years ago
5 0
<h2>Answer:</h2>

The correct answers are:

1)  f(x)=-5^x

2) f(x)=7-12x

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

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

The rate of change of a function in the interval [a,b] is calculated by:

Rate\ of\ change=\dfrac{f(b)-f(a)}{b-a}

We have: [a,b]=[0,2]

1)

f(x)=-5^x

Hence, we have:

f(2)=-5^2\\\\\\f(2)=-25

and

f(0)=-5^0\\\\\\f(0)=-1

Hence, the rate of change in the interval [0,2] is:

=\dfrac{-25-(-1)}{2-0}\\\\\\=\dfrac{-24}{2}\\\\\\=-12

Hence, option: (1) is correct.

2)

f(x)=7-12x

We know that for any linear function of the type y=mx+c

The rate of change in any interval =m

Here we have: m= -12

Hence, Rate of change= -12

Option: 2 is correct.

3)

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

f(2)=-3\times 3^2\\\\\\f(2)=-27

and

f(0)=-3\times 3^0\\\\\\f(0)=-3

Hence, Rate of change is:

=\dfrac{-27-(-3)}{2-0}\\\\\\=\dfrac{-24}{2}\\\\\\=-12

Hence, option: 3 is correct.

4)

f(x)=-12^x

f(2)=-12^2=-144

f(0)=-12^0=-1

Hence, rate of change is:

=\dfrac{-144-(-1)}{2-0}\\\\\\=\dfrac{-143}{2}

Option: 4 is incorrect.

5)

f(x)=-\dfrac{1}{12}x+9

It is linear function.

Hence\ ,\ rate\ of\ change=\dfrac{-1}{12}

Hence, option: 5 is incorrect.

6)

f(x)=12x-\dfrac{2}{3}

Again it is a linear function with rate of change: 12

Hence, option: 6 is incorrect.

Luden [163]3 years ago
3 0

Answer:

The answer is f(x) = 7 - 12x

Step-by-step explanation:

f(x) = 7 - 12x has average rate -12 on the interval [0 , 2] because:

f(0) = 7 - 12(0) = 7

f(1) = 7 - 12(1) = -5

f(2) = 7 - 12(2) = -17

The difference between 7 , -5 , -17 is constant and equal -12

∴ The average rate of change is -12

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