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
3
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