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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

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 class=

Sagot :

a) b) c) d)

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

[tex]\Delta=\frac{f(b)-f(a)}{b-a}[/tex]

2) So let's plug the functions:

[tex]\begin{gathered} a)\text{ }\Delta=\frac{(100)+2\text{ -\lbrack(0)+2\rbrack}}{100-0}=\frac{102-2}{100}=\frac{100}{100}=1 \\ b)\text{ }g(x)=2^x\text{ }\Delta=\frac{2^{100}-2^0}{100-0}=\frac{1.26\times10^{30}}{100}=1.26\times10^{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\times3^x\Delta=\frac{50,000-3^{100}-\lbrack50,000-3^0}{100}=-5.15\times10^{45} \\ e)q(x)=87.5 \end{gathered}[/tex]

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)

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