Question

Question 1(Multiple Choice Worth 6 points)

(07.06)

For the graphed function f(x) = −(3)x − 1 + 3, calculate the average rate of change from x = 1 to x = 3.

graph of f of x equals negative 1 times 3 to the x minus 1 power, plus 3.

−4
−2
2
4

Answer 1

Hence, the rate of change of f(x) from x=1 to x=3 is given by:

-4

Explanation:

We have to find the rate of change of the function f(x) from x=1 to x=3 which is defined as:

`f(x)=-(3)^(x-1)+3`

The rate of change of the function f(x) from x=1 to x=3 is given by:

`(f(3)-f(1))/(3-1)`

we know that:

`f(1)=-(3)^(1-1)+3\\\\f(1)=-(3)^0+3\\\\f(1)=-1+3\\\\f(1)=2`

Similarly,

`f(3)=-(3)^(3-1)+3\\\\f(3)=-(3)^2+3\\\\f(3)=-9+3\\\\f(3)=-6`

Hence, the rate of change is given as:

`(-6-2)/(3-1)\\\\=(-8)/(2)\\\\=-4`

Hence, the rate of change of f(x) from x=1 to x=3 is given by:

-4

Answer 2

The rate of the change for the function between points x=1 and x=3 will be given by:
[f(3)-f(1)]/(3-1)
f(3)=-6
f(1)=2

thus the rate of change will be:
(-6-2)/(3-1)
=-8/2
=-4
Answer: -4