Question

Question 1(Multiple Choice Worth 6 points)

Answer 1

Answer:

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

-4

Step-by-step 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:

$\dfrac{f(3)-f(1)}{3-1}$

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:

$\dfrac{-6-2}{3-1}\\\\=\dfrac{-8}{2}\\\\=-4$

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