Pre-TestUnit1:FunctionsKEY
No calculator necessary. Please do not use a calculator.
Determine if each of the following is a true function or not. Explain how you know. (4 pts; 2 pts for answer,
2 pts for explanation)
2. 1.
2
4
1
1
0
0
1
1
2
4
Function because it has one output per input.
Not a function. Consider 4 could have two outputs
namely 2 or 2.
3. Input: Type of an individual bird (robin, finch, etc.)
Output: That bird’s exact weight
4.
Not a function. Since we input the type of bird
and not the individual bird itself, you can get
multiple outputs. For example, one robin could
weight one pound and another robin could weigh
one and a half pounds.
Function
Vertical Line Test
5. 1, 3, 9, 27, 81 …
6. Give an example of a function in words explaining the
input, output, domain, range and how you know it is a
Function, it is a sequence
true function.
Answers will vary, but an example would be as follows:
Input: hours worked in a day at $10 per hour
Output: money made that day
Domain: 0hrs, 24hrs Range: $0, $240
Each input has only one output
Give the domain and the range of the following functions. (4 pts; 2 pts for each)
7. 4 7
8. Input: Teenager’s identity
Output: Weekly allowance as of today
: ∞, ∞
: 7, ∞
: 13 !", 19 !"
: 0, #$%! & '(()!%*+ $(
1
Given the functions ,- .-. / 0 and 12 23 . evaluate the following. (4 pts; 2 pts for correct input,
2 pts for correct answer)
9. 3
10. 42
3 12
42 10
Graph the following functions by filling out the 5/7 chart using inputs (5 values) that you think are appropriate.
(4 pts; 1 pt for appropriate 5 values, 1 pt for correct table, 2 pts for graph following table)
8
9
11. / 2
2
6
12. / 1
1
3
0
2
1
3
2
6
8
1
4
0
0
1
4
2
8
3
Answer the following questions using the given function showing the value of an investment in ten thousands of
dollars (;) based on the number of years from this year (<). (4 pts; partial credit at teacher discretion)
13. What does the point on the graph represent?
=
A $30,000 value after 4 years
14. Based on the graph, what is causing the value of the
investment to decrease and how do you know?
2
We can’t tell because the graph only shows value over time.
2
Calculate/estimate the average rate of change and the initial value over the interval ., . for each function.
(4 pts; 2 pts for each)
16. 3
15.
ROC: > 1
IV: 2
ROC: 0
IV: 3
17. A banker has been gaining $2,000 per year on an investment and expects to do the same the next few years.
The banker’s investment currently has a value of $18,000. Think of the function that shows how much money the
investment is worth based on how many years it has been since this year.
ROC: $2,000?((#
IV: 18,000
18.
ROC:
4
7
AB
2
4
0
1
2
2
4
5
IV: 1
For the following functions tell whether they are linear or non-linear, give the domain where they are increasing
and where they are decreasing, and then give the max or min of the function.
(4 pts; 1 pt for linear/non-linear, 2 pts for increasing/decreasing domain, 1 pt for max/min)
8
19. C 3
20. 3 / 5
Linear
Increasing domain: ∞, ∞
Decreasing domain: ∅
Max: ∅
Min: ∅
Non-linear
Increasing domain: ∞, 3
Decreasing domain: 3, ∞
Max: fx 5
Min: ∅
3
Use the following graph showing a function modeling the miles per gallon (G) a car gets in terms of its speed
(H) to answer the questions. (4 pts; partial credit at teacher discretion)
35$?I at 55$?4
22. What are all the possible speeds this car can drive at?
From 0mph to 110mph
Mileage in mpg
N
21. What appears to be the best mileage this car will get and at
what speed does it occur?
23. What are all the possible mileages this car can get?
From 0mpg to 35mpg
Speed in mph
M
Determine which graph matches the story and explain why. (5 pts; 2 pts for correct answer with no explanation)
24. I started to walk to class, but I realized I had forgotten my notebook, so I went back to my locker and then I
went quickly at a constant rate to class.
Graph C
Sketch a graph modeling a function for the following situations. (5 pts; partial credit at teacher discretion)
25. A dog is sleeping when he hears the cat “meow” in the next room.
He quickly runs to the next room where he slowly walks around looking
for the cat. When he doesn’t find the cat, he sits down and goes back
to sleep. Sketch a graph of a function of the dog’s speed in terms of
time.
4
Lesson 1.1
1.1
Unit 1 Homework Answer Key
Determine if each of the following is a true function or not and explain how you know. If it is a true function,
give the domain and range.
1. 2
4
1
1
0
0
1
1
2. / 25
4
O3
2
4
True function
: ∞, ∞, : 0, ∞
3. √ / 5
5
0
4
1
8
O6
Not a function
6
O8
0
O5
3
O4
4
O3
2
8
0
0
2
8
4
4
Not a function
8
4. 9 B 5
1
2
4
3
11
4
True function
: 5, ∞, : 0, ∞
5. / 100
3
O4
4
4
True function
: ∞, ∞, : ∞, ∞
6. 2 / 5
0
O10
6
O8
8
O6
2
1
1
3
0
5
1
7
2
9
True function
: ∞, ∞, : ∞, ∞
5
7. 8. 2 1
0
0
1
O1
4
O2
9
O3
25
O5
2
7
1
1
Not a function
True function
: ∞, ∞, : 1, ∞
9. 9
10.
5
O4
3
0
3
0
5
O4
Not a function
8
4
2
/
SR
9
1
1
2
7
1
2
0
0
O4
2
0
Not a function
11. QR
9
0
1
12. Q
2
1
0
0
2
1
4
2
2
1
1
2
1
2
2
1
True function
: ∞, ∞, : ∞, ∞
True function
: T 0, : T 0
13. Explain how to determine whether or not an
equation models a function.
If the variable has an exponent, it is not a
function.
14. Explain how to determine whether or not a
table models a function.
If there are multiple outputs for a single input, it is
not a function.
6
Determine if the following descriptions of relationships represent true functions and explain why they do or why
they do not. If it is a true function give a description of the domain and range.
15. Input: Time elapsed, Output: Distance run around the track.
Not a true function because different runners could have the same input but different outputs.
Domain: 0, ∞), Range:[0, ∞)
16. Input: Store’s name, Output: Number of letters in the name.
True function because the same name (and spelling) will yield only one output.
Domain: U!!V (*#$(, Range: U*'ℎ !(*W$X(
17. Input: Person’s age, Output: Yearly salary.
Not a true function because the same age could have the different outputs.
Domain: (0, $#%$W$#I((Y((#+ℎ("], Range: [0, $#%$W$(#!#!#]
18. Input: Amount of food eaten, Output: A dog’s weight.
Not a true function because the same amount of food could lead to different outputs.
Domain: [0, $#%$W$#$ W*V "? %X!(] Range: (0, ∞)
19. Input: Person’s name/identity, Output: That person’s birthday.
True function because each input will only have one output. People don’t have multiple birthdays.
Domain: U!!*#$( ?( ?!(, Range: #!!"#V(
20. Input: Person’s age, Output: Height.
Not a true function because the same age could have different heights.
Domain: (0, $#%$W$#I((Y((#+ℎ("], Range: (0, Vℎ(ℎ(%IℎV Vℎ(V#!!(V?( *]
21. Input: Name of a food, Output: Classification of that food (such as meat, dairy, grain, fruit, vegetable).
True function because every food has only one classification.
Domain: U!! ", Range: Z!#%%+#V% * "
22. Input: Time studied for test, Output: Test score.
Not a true function because people could study for the same amount of time but get different test scores.
Domain: 0, ∞), Range: [0, 100]
Determine if the following sequences represent true functions and explain why they do or why they do not. If it
is a true function give a description of the apparent domain and range.
23. 0,1,2,3,4,5 …
Function
Domain: [0, ∞)
Range: Integers greater than zero
24. 0, 1 0, 1 2, 3, 4, 5 …
Not a function, more than one output for an input
25. 0,1,0,1,0,1 …
Function
Domain: [0, ∞)
Range: Zero and one
26. 1,1,1,1,1,1 …
Function
Domain: [0, ∞)
Range: One
27. 0 1, 0 1, 0 1, 0 1, 0 1, 0 1 …
Not a function, more than one output for an input
28. 0,1,1,2,3,5 …
Function
Domain: [0, ∞)
Range: Fibonacci numbers
29. 1,2,4,8,16,32 …
Function
Domain: [0, ∞)
Range: Powers of two
30. 1,3,5,7,9,11 …
Function
Domain: [0, ∞)
Range: Odd numbers greater than zero
7
Evaluate the given functions at the given inputs.
,- -. / .
[
=M M3
12 \ 2 3
31. 2)
(−2) = 6
32. (10)
(10) = 102
33. (−3)
(−3) = 11
34. (0)
(0) = 2
35. ℎ(−2)
8
ℎ(−2) = −3
36. ℎ(−8)
ℎ(−8) = −5
37. ℎ(4)
ℎ(4) = −2
38. ℎ(0)
ℎ(0) = −3
39. Y(2)
Y(2) = 8
40. Y(−2)
Y(−2) = −8
41. Y(4)
Y(4) = 64
42. Y(1)
Y(1) = 1
8
Lesson 1.2
Graph the following functions by filling out the table using the given inputs (5 values).
8
1. 7
2
3
2. B / 2
1
6
0
7
1
6
2
3
9
0
8
1
5
2
0
3
7
4
8
5. ] / 2
10
0
6
0
3
1
0
2
3
3
6
4
1
1
0
1
1
1
2
7
6
1
3
2
2
3
9
4
4. 2 1
3. √ / 9
2
7
6. √ / 7
5
1
0
2
5
3
10
4
7
0
9
Graph the following functions by filling out the table using the inputs (5 values) that you think are appropriate.
7. 2 8
2
0
1
6
8. B 4
0
8
1
6
2
0
8
9. 4
4
6
7
0
6
8
3
6
0
4
3
2
6
0
4
2
1
3
8
4
0
4
1
3
2
0
10. √ / 8
2
5
0
4
2
3
4
2
6
1
8
0
7
1
12. / 4
11. √ / 7
3
2
2
3
9
4
2
0
1
3
10
13. Explain why it would be beneficial to use the inputs 2, −1, 0, 1, and 2 for the function () = + 1.
Answers may vary. The points are centered around the vertex of the parabola
B
14. Explain why it would be beneficial to use the inputs −8, −4, 0, 4, and 8 for the function () = − 2.
9
Answers may vary. The inputs are multiples of the denominator causing outputs to be whole numbers.
15. Explain why it would be beneficial to use the inputs −9, −8, −5, 0, and 7 for the function () = √ + 9.
Answers may vary. The inputs are chosen so that the number under the square root is a perfect square.
16. Explain how you would choose 5 different inputs for the function () = √ + 6. Explain why you feel these
are the best input values for this function.
Answers may vary. Choose values of so that + 6 is a perfect square. For example: −6, −5, −2, 3, 10
17. For problems 2, 5, 8, 9, describe a pattern in the change in the () values for each function.
Answers may vary. The () values increase by a constant amount.
18. For problems 2, 5, 8, 9, explain similarities and differences in the structure of the equations.
Answers may vary. All the equations follow the pattern = $ + X
19. For problems 2, 5, 8, 9, explain similarities and differences in the graph of each function.
Answers may vary. The graphs are all straight lines.
11
Lesson 1.3
Calculate or approximate the average rate of change of the following functions over the interval \, \ and
then again over the interval ., .. Finally, give the initial value.
1. 2 7
2. B 10
3. 2 7
. _. Z. 4, 4: 4
. _. Z. 4, 4: 6
. _. Z. 4, 4: 2
. _. Z. 2, 2: 4
. _. Z. 2, 2: 6
. _. Z. 2, 2: 2
`. a.:3
`. a. :0
`. a.:7
4. 10
5. 3 / 2
6. 9 3
. _. Z. 4, 4: 0
. _. Z. 4, 4: 3
. _. Z. 4, 4: 9
. _. Z. 2, 2: 0
. _. Z. 2, 2: 3
. _. Z. 2, 2: 9
`. a.:10
`. a. :2
`. a.:3
7.
8.
9.
. _. Z. 4, 4: 2
. _. Z. 4, 4: 9
. _. Z. 2, 2: > 9
. _. Z. 2, 2: 2
. _. Z. 2, 2: 9
`. a.:> 2.75
`. a. :6
`. a.:6
8
. _. Z. 4, 4: 9
8
B
B
B
B
B
12
10.
11.
. _. Z. 4, 4:
8B
b
. _. Z. 4, 4: ]
12.
8
9
. _. Z. 4, 4: 8
8
9
8
. _. Z. 2, 2: 9
. _. Z. 2, 2: 9
. _. Z. 2, 2: > 9
`. a.:9
`. a. :5
`. a.:> 2.75
13.
14.
15.
4
8
2
3
. _. Z. 4, 4: 1
4 2 0
6
5
4
8
. _. Z. 4, 4: . _. Z. 2, 2: 1
. _. Z. 2, 2: `. a. :0
`. a. :4
`. a. :3
16.
17.
18.
2 1
4 1
. _. Z. 4, 4: 0
0
0
2
1
4
0
2
3
4
2
1
1
2
4
2 1
3
4
. _. Z. 4, 4: 1
4
6
2
5
2
0
4
4
1
3.5
2
3
]
8
. _. Z. 2, 2: 0
5
0
3
. _. Z. 4, 4: 9
0
0
1
6
2
7
]
9
2 1 0
5 4.5 4
8
. _. Z. 4, 4: . _. Z. 2, 2: 0
. _. Z. 2, 2: 1
. _. Z. 2, 2: `. a. :0
`. a. :5
`. a. :4
8
13
19. A lawyer charges $50 an hour plus a flat attorney’s fee of $250.
. _. Z. 4, 4: 50
. _. Z. 2, 2: 50
`. a. :250
20. A man currently has $10,800 in an interest bearing account. Since the interest is simple and not compound,
he has been and will continue to make $100 per year in interest.
. _. Z. 4, 4: 100
. _. Z. 2, 2: 100
`. a. :10,800
21. A Star Wars enthusiast has to buy the same number of Star Wars toys each year as he already owns total. So
if he owns 30 currently, he would buy another 30 bringing his total up to 60. The following year he would have to
purchase 60 and so on. He currently has 16 Star Wars toys.
. _. Z. 4, 4:
255
31.875
8
. _. Z. 2, 2: 15
`. a. :16
22. What did you notice about the average rate of change over both intervals for problems 5, 11, and 17? What
do you think is the reason why that happened?
Answers may vary. The rate of change was the same on both intervals. This is because the function increases at a
constant rate.
23. What did you notice about problem number 4 and 16? Why did that happen? Graph both functions and then
try to determine why it would happen.
Answers may vary. The rates of change are both 0. The graph is symmetrical. The values are the same
whether is positive or negative because is squared.
14
Lesson
Lesson 1.4
Determine whether the following functions are linear or non-linear and explain how you know. Blank tables
and coordinate planes have been given to graph the functions if that helps you.
8
1. 2
non-linear
2. 2
linear
3. 2 / 2
linear
B
4. / 3
non-linear
7. √ / 9
5. 5 / 3 0
linear
non-linear
8. 3Q 2
6. 4 5
linear
non-linear
9. B non-linear
15
10. B 7
non-linear
11. 2Q / 3
12. √ 2
non-linear
non-linear
13. Give an example of a linear function in equation form.
Answers will vary. Sample: 2 / 1
14. Give an example of a linear function in table form.
Answers will vary. Sample:
1
2
2
4
3
6
4
8
5
10
15. Sketch an example of a linear function in graph form.
Answers will vary. Sample:
16. Give an example of a non-linear function in equation form.
Answers will vary. Sample: 17. Give an example of a non-linear function in table form.
Answers will vary. Sample:
1
1
2
4
3
9
4
5
16 25
18. Sketch an example of a non-linear function in graph form.
Answers will vary. Sample:
16
For each linear graph tell whether it is increasing, decreasing, or constant.
19. Increasing
20. Decreasing
21. Constant
22. Increasing
23. Increasing
24. Constant
25. Decreasing
26. Constant
27. Decreasing
28. Decreasing
29. Constant
30. Increasing
17
For each non-linear graph tell the domain where it is increasing and decreasing and identify any maximum,
minimum, local maximum, or local minimum.
31.
32.
33.
Increasing: 3, ∞
Decreasing: ∞, 3
Minimum: 7
Increasing: ∞, 2
Decreasing: 2, ∞
Maximum: 5
Increasing: ∞, 3#*"3, ∞
Decreasing: 3,3
Local Maximum: 22
Local Minimum: 14
34.
35.
36.
Increasing: ∞, 3#*"1, ∞
Decreasing: 3, 1
Local Maximum: 10
8
Local Minimum: > Increasing: 1, ∞
Decreasing: ∞, 1
Minimum: 2
Increasing: ∞, 5#*"3, ∞
Decreasing: 5,3
Local Maximum: > 80
Local Minimum: > 5
18
37.
38.
39.
Increasing: ∞, 3
Decreasing: 3, ∞
Maximum: 5
Increasing: 2, ∞
Decreasing: ∞, 2
Minimum: 4
Increasing: ∞, 1#*"2, ∞
Decreasing: 1,2
Local Maximum: > 1
Local Minimum: > 3
40.
41.
42.
Increasing: ∞, 4#*"2, ∞
Decreasing: 4,2
Local Maximum: > 17
Local Minimum: > 18
Increasing: ∞, 3#*"1, ∞
Decreasing: 3,1
Local Maximum: 14
Local Minimum: > 4
Increasing: ∞, 4
Decreasing: 4, ∞
Maximum: 7
19
Lesson 1.
1. 5
Use the following graph showing a function modeling the production cost per stembolt (c) a factory gets in
terms of the production rate of how many stembolts it produces per minute (d) to answer the questions.
Production Rate (stembolts per minute) (f)
1.
If the possible inputs for this function are between one
and nine, what does that mean in the context of this problem?
The factory can produce between 1 and 9 stembolts per minute.
2.
Within those inputs, what are all the different costs per
stembolt that the company could have?
1 to 6 dollars per stembolt.
3.
At what production rate does the company get the
cheapest production cost?
5 stembolts per minute.
4.
What is the cheapest production cost?
1 dollar per stembolt.
5.
Between what production rates does the company get
cheaper and cheaper production costs?
Between 1 and 5 stembolts per minute.
6.
Between what production rates does the company get
higher and higher production costs?
Between 5 and 9 stembolts per minute.
Use the following graph showing a function modeling the company’s weekly profit in thousands of dollars (e) in
terms of the number of weekly commercials it airs (c) to answer the questions.
Number of Weekly Commercials (g)
7.
What inputs make sense in the context of this problem?
Between 20 and 80 weekly commercials.
8.
What are all the different profits that the company could
have?
0 to $80,000
9.
How many weekly commercials gives the best profit for
the company?
50 weekly commercials
10. What is the best profit the company can expect?
$80,000
11. Between how many weekly commercials does the
company get better and better profits?
Between 20 and 50 weekly commercials.
12. Between how many weekly commercials does the
company get worse and worse profits?
Between 50 and 80 weekly commercials.
20
Use the following graph showing a function modeling a man’s stock market investment value in thousands of
dollars (;) in terms of his age (h) to answer the questions.
13. If the man began investing at 20 years old and retired at
the age of 80 (at which point he sold all his stocks), what inputs
make sense in the context of this problem?
20 to 80
14. What are all the different investment values the man had
during the time he was investing?
$25,000 to $75,000
15. At what age was his investment value the highest? How
high was it?
30 years old; $75,000
16. At what age was his investment value the lowest? How
low was it?
70 years old; $25,000
17. Between what ages was his investment growing in value?
Between 20 and 30 and then between 70 and 80.
18. Between what ages was his investment losing value?
Between 30 and 70.
19. Overall, since he started investing at 20 years old and retired at 80 years old, did he make or lose money?
How much?
He lost about $30,000 since he started with $65,000 and retired with $35,000.
20. What appears to be the earliest age he should have retired (after 80 years old) in order to have at least
broken even on his investments?
Somewhere around 87 or 88 years old.
Use the following graph showing a function modeling the penguin population in millions (e) in terms of average
temperature of the Antarctic in degrees Fahrenheit (<) to answer the questions.
21. What inputs make sense in the context of this problem?
Between 100 and 20 degrees.
22. What are all the different populations that the penguins
could have?
0 to 8 million
23. What average temperature gives the highest penguin
population?
40 degrees
24. What is the highest population of the penguins?
8 million
25. Between what temperatures does the population grow?
Between 100 and 40 degrees.
26. Between what temperatures does the population shrink?
Between 40 and 20 degrees.
21
Lesson 1.6
Match each description with its function graph showing speed in terms of time.
speed
speed
time
A.
speed
time
B.
time
C.
1. A squirrel chews on an acorn for a little while before hearing a car coming down the street. It then runs quickly
to the base of a nearby tree where it sits for a second listening again for the car. Still hearing the car, the squirrel
climbs up the tree quickly and sits very still on a high branch. i#?4Z
2. A possum is slowly walking through a backyard when a noise scares it causing it to hurry to a hiding place. It
waits at the hiding place for a little while to make sure it’s safe and then continues its slow walk through the
backyard. i#?4U
3. A frog is waiting quietly in a pond for a fly. Noticing a dragonfly landing on the water nearby, the frog slowly
creeps its way to within striking distance. Once the frog is in range, it explodes into action quickly jumping
towards the dragonfly and latching onto with its tongue. The frog then settles down to enjoy its meal. i#?4j
Match each description with its function graph showing height in terms of time.
height
height
time
D.
height
time
E.
time
F.
4. Sean starts to bike up a long steep hill. Half way up, he gets off his bike to walk the rest of the hill. When he
makes it to the top, he races down the other side until he makes it to the bottom. i#?4
5. Micah is racing down a flat road. He comes to a small hill and charges up as fast as he can. Coming down the
other side, Micah gains speed for the big hill ahead. Micah climbs the hill to the top, and hops off his bike to
stretch. i#?4k
6. Jerika hops on her bike as she comes out of her garage which sits at the top of a large hill. She coasts down the
hill and starts pedaling as the road flattens. She realizes she forgot something, so she rides back up to her house.
i#?4l
22
Match each description with its function graph showing speed in terms of time.
speed
speed
time
G.
speed
time
H.
time
I.
7. Sean starts to bike up a long steep hill. Half way up, he gets off his bike to walk the rest of the hill. When he
makes it to the top, he races down the other side until he makes it to the bottom. i#?4`
8. Micah is racing down a flat road. He comes to a small hill and charges up as fast as he can. Coming down the
other side, Micah gains speed for the big hill ahead. Micah climbs the hill to the top, and hops off his bike to
stretch. i#?4m
9. Jerika hops on her bike as she comes out of her garage which sits at the top of a large hill. She coasts down the
hill and starts pedaling as the road flattens. She realizes she forgot something, so she turns around and rides back
up to her house. i#?4i
Sketch a graph modeling a function for the following situations.
10. A runner starts off her day running at an average speed down her street.
At the end of a street is a slight hill going down so she runs even faster down
the hill. At the bottom of the hill she has to go back up to the level of her
street and has to slow way down. Sketch a graph of a function of runner’s
speed in terms of time. i#?4$#Y#
11. A runner starts off her day running at an average speed down her street.
At the end of a street is a big hill going down, so she runs very fast down the
hill. At the bottom of the hill she runs on flat ground at an average speed for a
while before going back up another hill where she slows way down. Sketch a
graph of a function of runner’s height in terms of time. i#?4$#Y#
23
12. A fish swims casually with her friends. All of a sudden, she hears a boat,
so she darts down toward the bottom of the ocean and hides motionlessly
behind the coral. She remains still until she hears the boat pass. When the
coast is clear, she goes back to swimming with her friends. Sketch a graph of
a function of the fish’s speed in terms of time.i#?4$#Y#
13. My dad drove me to school this morning. We started off by pulling out of
the driveway and getting on the ramp for the interstate. It wasn’t long before
my dad saw a police car, so he slowed down. The police car pulled us over, so
we sat on the side of the road until the cop finished talking to my dad. Sketch
a graph of a function of the car’s speed in terms of time. i#?4$#Y#
14. Rashid starts on the top of a snow-covered hill. He sleds down and coasts
on flat ground for a few feet. Tickled with excitement, Rashid runs up the hill
for another invigorating race. About half way up the hill, he recognizes a
friend of his has fallen off his sled. Rashid stops to help his friend and begins
slowly pulling his friend back up the hill. Tired, Rashid and his friend finally
make it to the top of the hill. Sketch a graph of a function of Rashid’s height
in terms of time. i#?4$#Y#
15. Roller coaster cars start out by slowly going up a hill. When all of the cars
reach the top of the hill, the cars speed down the other side. Next, the cars
are pulled up another, but smaller, hill. Racing down the other side, the cars
race through a tunnel and come to a screeching halt where passengers are
unloaded. Sketch a graph of a function of the roller coaster cars’ speed in
terms of time. i#?4$#Y#
24
16. A dog is sitting on his owner’s lap. When the owner throws the ball, the
dog sprints after the ball and catches it mid-air. The dog trots back and plops
back on the owner’s lap. The owner throws the ball again; tired, the dog jogs
over to the ball and lies down next to it. Sketch a graph of a function of the
dog’s speed in terms of time. i#?4$#Y#
17. A function starts out increasing slowly then it increases faster and faster
before hitting a maximum spike about halfway through the graph. From the
spike it decreases quickly and then decreases slower and slower before finally
leveling out toward the end of the graph. i#?4$#Y#
18. A function starts off very high and stays level for a little while. It then
drops quickly to about the halfway mark and stays level again for a little while.
It then drops very close to the bottom and stays level after that.
i#?4$#Y#
25
ReviewUnit1:FunctionsKEY
No calculator necessary. Please do not use a calculator.
Determine if each of the following is a true function or not. Explain how you know.
1. / 100
8
6
0
6
O6
O8
O10
O8
Not a function
Multiple outputs for a given input
8
2. 6
8
O6
4
2
2
4
Function
One output for each input
0
6
2
4
4
2
3. Input: Number of candy bars purchased
Output: Amount of money spent
Function
One output for each input
4. Input: Age of a person
Output: Number of hours spent playing video games
Not a function
Multiple outputs for a given input
5. Function, one output for each input
6. Not a function, multiple outputs for a given input
7. 6,3,0, 3, 6 …
Function
One output for each input
8. 2, 4, 6 8, 8 16, 10 32 …
Not a function
Multiple outputs for a given input
9. Give an example of a function in words explaining the input, output, domain, range and how you know it is a
true function.
Answers may vary.
26
Give the domain and the range of the following functions.
10. 3 5
11. √ / 6 3
12. Input: Number of students in
the class
Output: Number of birthdays
in the class
: ∞, ∞
: 6, ∞
: 0, ∞
: 5, ∞
: 3, ∞
: 0, ∞
[
Given the functions ,- 3 - \ and 12 2. / 0 evaluate the following.
13. 3 3
14. 6 6
15. 43 3
16. 42 2
Graph the following functions by filling out the 5/7 chart using inputs (5 values) that you think are appropriate.
18. 5
17. √ / 8
8
0
7
1
4
2
1
3
8
4
2
1
1
4
0
5
1
4
2
1
27
Calculate/estimate the average rate of change and the initial value over the interval ., . for each function.
20. B 2
19.
R.O.C.: 2
R.O.C.: 0
IV: 0
IV: 7
21. A homeowner made a down payment of $10,000 and pays $700 each month for his mortgage. Think of the
function that shows how much money has been spent on the house in terms of the number of months it has been
owned. R.O.C.: 700 IV: 10,000
22.
R.O.C.:
8]
9
2
1
1
2
0
4
1
8
2
16
IV: 4
For the following functions tell whether they are linear or non-linear, give the domain where they are increasing
and where they are decreasing, and then give the max or min of the function.
23. y x 5 / 2
Non-linear
Increasing: ∞, 5
Decreasing: 5, ∞
Max: y 2
24. y 5x 3
Linear
Increasing: ∞, ∞
28
Answer the following questions using the given function modeling the height (o) of an angry bird that is thrown
in terms of time (t) in seconds to answer the questions.
26. Based on the graph, what is causing the height of the bird to
decrease, and how do you know?
We don’t know because the graph doesn’t give us that information.
27. What is the maximum height of the angry bird and when does
the bird reach its max height?
8V at 1(+
Height in feet 1
25. What does the point on the graph represent?
6 feet high after 1.5 seconds
28. What inputs makes sense in this context?
0V 2(+ *"
29. During what times is the bird’s height increasing?
Between 0#*"1(+
Time in seconds 2
30. What are all the different heights the bird reaches?
From 0V 8V
Determine which graph matches the story and explain why.
31. A young boy decided he was fed up with his parents and wanted to join the circus. After gathering his
belongings in a hobo-style bag on a stick, he started running away from home very fast. He continually slowed
down the longer he ran until he finally stopped about halfway to the circus when he realized he was being
irrational.
Graph iii
29
Sketch a graph modeling a function for the following situation.
Height
32. A seed was planted in the early spring. A sprout appeared and grew rapidly in the rainy spring. Growth
nearly stopped during the dry and hot summer. In the middle of the summer, a rabbit ate the plant. Sketch a
graph of a function of the plant’s height in terms of time.
Time
30