3.09 Unit Test Using Function Models

Question: Graph the functions on the same coordinate plane.

f(x)=7

g(x)=x^2+2x−8

What are the solutions to the equation f(x)=g(x)?

Answer: -5

Question: What are the relative minimum and relative maximum values over the interval [1, 5] for the function shown in the graph?

Answer: relative minimum = −14 , relative maximum = −3

(lowest part of curve is at (4.5,-14))

Question: Which characteristic is correct for the function

f(x)=−2x^3+3x^2 ?

Answer: neither even nor odd

Question: The graph shows the miles biked for each week of training.

Which statements are true?

Answer: The graph is decreasing between the first and seventh week.

More miles were biked initially than the tenth week.

Question: The function f(x) is the total amount spent at a store, when purchasing x items that are $5 each and the items are not taxable.

What is the practical domain for the function f(x)?

Answer: all whole numbers

Question: Consider two functions: g(x)=20(1.5)x and the function f(x) shown in the table.

x f(x)

−5 −45

−4 −48

−3 −49

−2 −48

−1 −45

0 −40

1 −33

Which statements are true?

Answer: g(x) has a greater y-intercept than f(x) does.

f(1) is less than g(−1) .

Question: The table of values represents a polynomial function f(x).

2 39

3 125

4 287

5 549

6 935

7 1469

How much greater is the average rate of change over the interval [5, 7] than the interval [2, 4] ?

Answer: 336

Question: What is (f+g)(x)?

f(x)=x^2−36

g(x)=x^3+2x^2−10

Answer: x^3+0x-46

Question: What is (f⋅g)(x)?

f(x)=x^4−9

g(x)=x^3+9

Answer: x^7+9x^4-9x^3-81

Question: What is (f−g)(x)?

f(x)=x^3−2x^2+12x−6

g(x)=4x^2−6x+4

Answer: x^3-6x^2+18x-10