Name________________________________ Date___________ Period ________
Final Review Part 1
Suppose that you go on a diet and the following graph displays your progress in losing weight. As seen in the
graph, your weight (w) is a function of the time since your diet started (t = 0) because each week results in only
one weight (in pounds).
1. Evaluate w(2). Explain in a complete sentence what your solution means in its real-world context.
A.
B.
C.
D.
w(2) = 170.
w(2) = 166.
w(2) = 162.
w(2) = 158.
The solution means that you weigh 170 pounds after 2 weeks.
The solution means that you weigh 166 pounds after 2 weeks.
The solution means that you weigh 162 pounds after 2 weeks.
The solution means that you weigh 158 pounds after 2 weeks.
2. Find a value of t such that w(t) = 158. Explain in a complete sentence what your solution means in its
real-world context.
A.
B.
C.
D.
t = 6.
t = 7.
t = 8.
t = 9.
The solution means that you weigh 158 pounds after 6 weeks.
The solution means that you weigh 158 pounds after 7 weeks.
The solution means that you weigh 158 pounds after 8 weeks.
The solution means that you weigh 158 pounds after 9 weeks.
3. Give a practical domain and range for the function w(t).
A.
B.
C.
D.
A practical domain would be all real numbers and a practical range would be all real numbers.
A practical domain would be all real numbers and a practical range would be 150-170 pounds.
A practical domain would be 0 to 10 weeks and a practical range would be all real numbers.
A practical domain would be 0 to 10 weeks and a practical range would be 150-170 pounds.
4. The table below shows per capita spending on prescription drugs in the United States. Using the data
in the table, estimate the per capita spending on prescription drugs in 1996. (Use the average rate of
change between the two consecutive data points that have years closest to 1996.)
Year
t
Per Capita Spending
on Prescription Drugs
(dollars)
D
1990
158
1995
224
1998
311
2000
423
2002
552
A.
B.
C.
D.
$253
$340
$237
$423
A certain math teacher recently purchased a 2015 Volkswagen Golf (a sensible choice since it is the 2015
Motor Trend Car of the Year) for $19,815. He was told that his monthly loan payment would be $357.22 for 5
years after he puts down a $1000 down payment.
5. Write a formula for the total amount he has paid toward the cost of the car (including down
payment), T, as a function of the number of months he has made payments on the loan, m.
A.
B.
C.
D.
T(m) = 2015 + 19,815
T(m) = 5m + 19,815
T(m) = 19,815m + 1,000
T(m) = 357.22m + 1,000
6. What will be the total cost of the car, after he has made all of the payments?
A.
B.
C.
D.
$19,815.00
$20,815.00
$22,433.20
$215,547.40
7. How much money will he pay in interest?
A.
B.
C.
D.
$2,618.20
$1,000.00
$22,433.20
$17,128.95
8. Following the recent debate among Republican Presidential candidates, the L.A. Times reported that
Donald Trump “increased his Twitter follower count by . . . 22,000 during the debate.”
Use function notation to represent the number of Donald Trump’s Twitter followers, A, after the
debate as a function of the number of Twitter followers, B, that he had before the debate.
A. A(B) = A + 22,000
B. A(B) = B + 22,000
C. A(B) = A - 22,000
D. A(B) = B - 22,000
1
9. Graph the line that passes through the point (-1,4) and is parallel to the line 𝑦 = 2 𝑥 − 5.
A.
B.
C.
D.
The General Sherman Tree in Sequoia National Park is the largest tree by volume in the world. As of 2015, it is
275 feet tall and 36.5 feet (438 inches) in diameter at its base. And it is still growing! The tree adds 0.4 inches
to its diameter each year.
10. Construct a linear formula that models the diameter of the General Sherman Tree, where d is the
diameter at the base and t is the number of years since 2015.
A.
B.
C.
D.
𝑑(𝑡)
𝑑(𝑡)
𝑑(𝑡)
𝑑(𝑡)
=
=
=
=
275𝑡 + 438
0.4𝑡 + 438
36.5𝑡 + 0.4
2015𝑡 + 275
11. Use the formula from part (a) to predict the diameter of the General Sherman Tree in the year 2100.
A.
B.
C.
D.
472
34
275.4
438.4
The data in the table below were collected by the U.S. Department of Health and Human Services and indicate
the rate of births to teenage mothers since 1991. Use the data in the table to answer the following questions.
Years Since
1991
t
0
3
6
9
12
15
18
21
Birth rate per 1,000
teenage girls
B
61.8
58.2
51.3
47.7
41.1
41.1
37.9
29.4
12. Find a linear regression model for these data.
A. 𝐵(𝑡) = −1.49𝑡 + 61.87
B. 𝐵(𝑡) = 1.49𝑡 + 61.87
C. 𝐵(𝑡) = −1.49𝑡 − 61.87
D. 𝐵(𝑡) = 1.49𝑡 − 61.87
13. Using the model found in question 12, interpret the practical meaning of the slope of the model.
A. The teen birth rate is decreasing by 1.49 every year.
B. The teen birth rate is increasing by 1.49 every year.
C. The teen birth rate is decreasing by 61.87 every year.
D. The teen birth rate is increasing by 61.87 every year.
14. Use the linear regression model to predict the Teen Birth Rate in 2001. (Round your answer to one
decimal place.)
A.
B.
C.
D.
26.1
46.8
12.3
14.9
15. Use the linear regression model to predict the Teen Birth Rate in 2015. (Round your answer to one
decimal place.)
A.
B.
C.
D.
26.1
46.8
12.3
14.9
16. Which of the following statements is false?
1.
2.
3.
4.
A concave up graph has an increasing rate of change.
All nonlinear functions have inflection points.
A linear graph has a constant rate of change.
A concave down graph has a decreasing rate of change.
17. A table of values is shown below.
x
5
6
7
8
9
y
-1
5
14
26
41
Which of the following is false about the table data?
A.
B.
C.
D.
The data represents a quadratic function.
The data has a constant rate of change.
The graph of the data is concave up.
The second differences are constant.
18. Which of the following graphs represents the function 𝑓(𝑥) = (x + 2)2 − 1.
A.
B.
C.
D.
An annual tradition at the University of Colorado is the egg drop, in which students build a container for an egg
that will be dropped from the eighth floor of the engineering building. The fall of a certain container could be
modeled by the following equation:
ℎ(𝑡) = −10𝑡 2 + 90,
where ℎ(𝑡) represents the height of the container in feet after 𝑡 seconds.
19. After how many seconds will the container hit the ground?
A.
B.
C.
D.
2 seconds
3 seconds
4 seconds
5 seconds
20. Evaluate ℎ(0). What does this value tell you? Explain in the context of the problem.
A.
B.
C.
D.
ℎ(0) = −10. This means that the height is 0 after -10 seconds.
ℎ(0) = 72. This means that the height is 72 after 0 seconds.
ℎ(0) = 90. This means that the height is 90 after 0 seconds.
ℎ(0) = 3. This means that the height is 0 after 3 seconds.
Kordell Stewart, a quarterback for the University of Colorado in the early 1990s, threw one of Mr. Farrington’s
favorite touchdown passes of all time to beat the University of Michigan in 1994. The pass was in the air for a
full three seconds before being tipped 6 feet off the ground and then caught for a touchdown. The height (in
feet) above the ground of the football can be modeled by ℎ(𝑡) = −16𝑡 2 + 𝑣𝑡 + 𝑘, where 𝑣 is the initial
velocity (in feet per second) when the ball left Stewart’s hand and k is the initial height (in feet). Because of
Stewart’s height and his stance at the time of the pass, we will say 𝑘 = 6.
21. Use the fact that the ball was tipped 6 feet off the ground after 3 seconds to find the value of 𝑣 and
write the equation for the function ℎ(𝑡) in standard form.
A.
B.
C.
D.
ℎ(𝑡) = −16𝑡 2 + 3𝑡 + 6
ℎ(𝑡) = −16𝑡 2 + 36𝑡 − 6
ℎ(𝑡) = −16𝑡 2 + 6𝑡 + 3
ℎ(𝑡) = −16𝑡 2 + 48𝑡 + 6
22. Find the vertex for the function ℎ(𝑡) and explain what this point means in the context of the problem.
A.
B.
C.
D.
(1.5, 42). After 1.5 seconds, the ball reached its maximum height of 42 feet.
(3, 6). After 3 seconds, the ball reached its maximum height of 6 feet.
(−1.5, 42). After 1.5 seconds, the ball reached its minimum height of 42 feet.
(6,3 ). After 6 seconds, the ball reached its minimum height of 3 feet.
Given the function f (x ) , calculate the inverse f
23. f ( x)  3 x  1
A. 𝑓 −1 (𝑥) = 𝑥 − 3
1
1
B. 𝑓 −1 (𝑥) = 3 𝑥 − 3
3
C. 𝑓 −1 (𝑥) = √𝑥 + 1
D. 𝑓 −1 (𝑥) =
24. f ( x) 
𝑥+1
3
2
x4
5
5
𝑥 + 10
2
2
4
B. 𝑓 −1 (𝑥) = 5 𝑥 − 5
5
5
C. 𝑓 −1 (𝑥) = 2 𝑥 − 2
2
D. 𝑓 −1 (𝑥) = 𝑥 + 4
5
A. 𝑓 −1 (𝑥) =
25. f ( x) 
7x  5
4
A. 𝑓 −1 (𝑥) = 4𝑥 + 10
4
5
B. 𝑓 −1 (𝑥) = 7 𝑥 − 7
C. 𝑓 −1 (𝑥) =
D. 𝑓 −1 (𝑥) =
4𝑥+5
7
1
5
𝑥+4
7
1
( x) .
Let 𝑓(𝑥) = 2𝑥 – 1, 𝑔(𝑥) = 3𝑥, and ℎ(𝑥) = 𝑥 2 + 1. Compute the following:
26. 𝑓(𝑔(𝑥))
A.
B.
C.
D.
6𝑥 − 3
9𝑥 2 + 1
3𝑥 2 − 1
6𝑥 − 1
27. ℎ(𝑔(𝑥))
A.
B.
C.
D.
6𝑥 − 3
9𝑥 2 + 1
3𝑥 2 − 1
6𝑥 − 1
28. ℎ (𝑔(𝑓(5)))
A. 9
B. 27
C. 730
D. 99
29. 𝑓 (𝑔(ℎ(3)))
A. 49
B. 59
C. 89
D. 99
30. If two functions are inverses of each other, then their composites, 𝑓(𝑔(𝑥)) and 𝑔(𝑓(𝑥)), should equal:
A. 1
B. 0
C. 𝑥
D. None of these