Question

Problem ID: PRABMVM9 For each of the functions f, g, h, P, and q, the domain is o sxs 100. For which functions is the average rate of change a good measure of how the function changes for this domain? Select all that apply. A. F(x)=x+2 B. g(x)=2* C. h(x)= 111x-23 D. p(x)=50,000 x 3% E. g(x)= 87.5

Answer 1

If you go off of the explanation below... the actual answers are A, C, E...

Explanation:

Correct Answer

A)

f(x)=x+2

C)

h(x)=111x−23

E)

q(x)=87.5

Answer 2

a) b) c) d)

1) Examining each function, let's test considering that the average rate of change is given by:

`\Delta=(f(b)-f(a))/(b-a)`

2) So let's plug the functions:

`\begin{gathered} a)\text{ }\Delta=\frac{(100)+2\text{ -\lbrack(0)+2\rbrack}}{100-0}=(102-2)/(100)=(100)/(100)=1 \\ b)\text{ }g(x)=2^x\text{ }\Delta=(2^(100)-2^0)/(100-0)=(1.26*10^(30))/(100)=1.26*10^(28) \\ c)\text{ }h(x)\text{ = }111x-23\text{ }\Delta=\frac{111(100)-23\text{ -\lbrack{}111(0)-23}}{100}=111 \\ d)\text{ }p(x)\text{ = }50,000*3^x\Delta=(50,000-3^(100)-\lbrack50,000-3^0)/(100)=-5.15*10^(45) \\ e)q(x)=87.5 \end{gathered}`

3) Since the average rate of change is a "measure of how much a function changes in the given interval" and considering that we have linear and exponential functions and the last one e) is not a function but an equation.

Then we can say that for the functions below the average rate of change is a good measure, not applying for the last one which, indeed is not a function.

a)

b)

c)

d)