For graph: y < 50 + 4x and y < 100 (horizontal line)
98. Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and the earrings cost $3. She needs to make at least $60. Sarah knows she will sell more than 10 bracelets. Write inequalities to represent the income from jewelry sold and number of bracelets sold.
2b + 3e ≥ 60 and b ≥ 10 OR 2x + 3y ≥ 60 and x ≥ 10
Equation to graph: y ≥ 2/3x + 20
Unit 3: Linear and Exponential Functions
A.REI.10,11: Represent and Solve Equations and Inequalities Graphically
99. Cameron is going to the candy store. He can buy chocolate and jelly beans. He has $30 to spend on candy. If chocolate costs $3 per pound and jelly beans cost $5 per pound, what are the different combinations of candy that he can purchase if he spends exactly $30?
x = chocolate, y = jelly beans
5 chocolates, 3 jelly beans
What if Cameron is going to spend no more than $30 on candy? What are the different combinations of candy he can purchase?
(0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (2, 1) (2, 2) (2, 3) (2, 4) (3, 1) (3, 2) (3, 3) (3, 4) (4, 1) (4, 2) (4, 3) (5, 1) (5, 2) (5, 3) (6, 1) (6, 2) (7, 1) (8, 1) (10, 0)
100. Consider the equations y = x + 4 and y = 2x – 2. What is the ordered pair solution to the system of equations? Graph them on the coordinate plane.
(2, 2)
101. Graph the inequality x – 3y ≥ 9
y ≤ 1/3x – 3
102. Graph the inequality –x + y < 4
y < x + 4
103. What equations correspond with the graphs shown?
y = 2x – 5 y = 1/3x + 4
104. Which equation corresponds to the points in the coordinate plane?
y = 1/2x
105. Based on the tables, what common point do the equations y = 2x + 2 and y = x – 4 share? (2, 2)
x

0

1

2

3

4

y

2

0

2

4

6

x

0

1

2

3

4

y

4

3

2

1

0

F.IF.1,2,3: Understand Concept of Function, Function Notation
106. Given f(x) = 2x – 4, find f(4) and f(6).
f(4) = 4 and f(6) = 16
107. Given f(x) = 4x + 1, find f(5) and f(0).
f(5) = 21 and f(0) = 1
108. If g(8) = 4 + 3(8), find g(x).
g(x) = 4 + 3x
109. If h(2) = 3(2), find h(x).
H(x) = 3x
110. If f(3) = 5 – 2(3), find f(x).
f(x) = 5 – 2x
111. Graph the function f(x) = 3x + 1 on the coordinate plane.
112. A hotdog vendor keeps track of his weekly costs by using the cost function C(x) = 450 + 1.5x, where x is the number of hot dogs sold.
a) What is the domain of the cost function? (think real world)
all whole #s greater than 0
b) What is the cost of selling 500 hot dogs in a week?
$1200
c) If his costs must be below $800 this week, what is the greatest number of hot dogs he can sell?
233 hot dogs
113. A tshirt company keeps track of its monthly costs using the cost function C(x) = 1000 + 8x, where x is the number of tshirts sold.
a) What is the domain of the cost function?
all whole #s greater than 0
b) What is the cost of selling 500 tshirts in a month?
$5000
c) If the company’s costs must be under $8000 this month, what is the maximum number of shirts
they can sell?
875 shirts
114. Consider the sequence: 3, 8, 13, 18, 23, …
a) Is this a finite or infinite sequence?
infinite
b) What is a_{1}? What is a_{4}?
a_{1} = 3 and a_{4} = 18
c) What is the domain of the sequence? What is the range of the sequence?
domain {1, 2, 3, 4, 5,…} range {3, 8, 13, 18, 23,…]
115. Given the function f(n) = 2n + 3, create a table for the sequence for the first 5 terms. What is the domain of the sequence? What is the range of the sequence?
domain {1, 2, 3, 4, 5} range {1, 1, 3, 5, 7}
116. Write a function that represents this sequence (hint: use arithmetic sequences)
n

1

2

3

4

5

a_{n}

2

1

4

7

10

f(n) = 3n  5
117. What function is modeled in this table?
x

1

2

3

4

5

F(x)

1

3

5

7

9

f(n) = 2n  1
118. What function is modeled in this table?
x

1

2

3

4

5

F(x)

2

9

16

23

30

f(n) = 7n  5
119. Which explicit formula describes the pattern in this table? C
n

1

3

4

6

9

P

2.48

7.44

9.92

14.88

22.32

a) n = P x 2.48 b) n = P + 2.48 c) P = n x 2.48 d) P = n / 2.48
120. Which explicit formula describes the pattern in this table? B
t

2

5

7

8

10

V

10.54

26.35

36.89

42.16

52.7

a) V = t x 10.54 b) V = t x 5.27 c) t = V x 5.27 d) t x V = 5.27
121. If f(11) = 2(11) – 6, which function gives f(x)?
f(x) = 2x  6
122. If g(4) = 5 – 3(4), which function gives f(x)?
g(x) = 5 – 3x
123. If h(9) = (9)^{2} – 1, which function gives h(x)?
h(x) = x^{2}  1
F.IF.4,5,6: Interpret Functions that arise in applications in terms of context
124. In 1985, there were 285 cell phone users in the town of Centerville. The amount of cell phone users in Centerville can be represented by the function A(t) = 285(1.75)^{t}, where A(t) is the number of cell phone users and t is the number of years after 1985. (be specific about whole #s v. real #s)
a) What are the yintercepts of the function A(t)?
(0, 285)
b) What is the domain of the function A(t)?
all whole #s greater than 0
c) Why are all the tvalues nonnegative?
can’t have negative years
d) What is the range of A(t)?
all whole numbers greater than 285
e) Does A(t) have a maximum or minimum value?
minimum is 285
125. Each year the country club sponsors a tennis tournament. The tournament starts with 128 players. Each round, half of the players are eliminated. The number of players in the tournament can be represented by the function P(t) = 128(1/2)^{t}, where P(t)represents the number of players and t represents the number of rounds. A portion of the graph of P(t) is shown below. (be specific about real #s or whole #s)
a) Even though it is not shown, what is the yintercept of P(t)?
(0, 128)
b) Is the function increasing or decreasing?
decreasing
c) Is the function positive or negative?
positive
d) What is the domain of P(t)? What is the range?
all whole numbers between 0 and 128
126. A company uses the function P(x) = 20x + 500 to represent the number of employees, P(x), after x number of years. Use the table of values shown below to answer the questions.
x

0

1

2

3

4

P(x)

500

520

540

560

580

a) What is the yintercept of the function? (0, 500)
b) Does the graph of the function have an xintercept? (no
c) Does the function increase or decrease? increase
127. Harold bought a boat and is using the function C(x) = 32,000 – 1,680x to represent the depreciation of the boat, where C(x) is the value of the boat and x is the number of years after its purchase. Use the table of values shown below to answer the questions.
x

0

1

2

3

4

C(x)

32,000

30320

28640

26960

25280

a) What is the yintercept of the function? (0, 32000)
b) Does the graph of the function have an xintercept? What is it? yes, (19.05, 0)
c) Does the function increase or decrease? decrease
128. A farmer owns a tractor that can consistently run an average of 15 miles an hour for up to 9 hours. Let y be the distance the tractor can travel for a given x amount of time in hours. The tractor’s progress can be modeled by a function. What is the domain of the function?
0 ≤ x ≤ 9 hours
129. A production team can consistently make an average of 100 bottles per hour for up to 10 hours. Let y be the total number of bottles the team makes for a given x amount of time in hours. The team’s progress can be modeled by a function. What is the domain of the function?
0 ≤ x ≤ 10
130. The graph below shows the height of a rock dropped from a cliff. The yaxis represents height of the rock and the xaxis represents the number of seconds after it was dropped.
a) What was the initial height of the rock?
about 100 feet
b) After how many seconds was the rock 50 feet in the air?
1 second
c) After how many seconds was the rock about 12 feet in the air? 3 seconds
d) How long did it take the rock to reach the ground?
10 seconds
F.IF.7, 9: Analyze Functions using different representations
131. Given the function f(x) = , identify the following: domain, range, yintercepts, xintercepts, maximum/minimum, increasing or decreasing, rate of change, end behavior, positive/negative.
domain: all real numbers; range: all real numbers; yintercept (0, 2); xintercept (4, 0); no max or min; decreasing; rate of change is 1/2; end behavior is up on the left and down on the right; both positive and negative
132. Given the function f(x) = , identify the following: domain, range, yintercepts, xintercepts, maximum/minimum, increasing or decreasing, rate of change, end behavior, positive/negative.
domain: all real numbers; range: all numbers greater than 0; yintercept (0, 1); no xintercept; no max or min; decreasing; approaches infinity on left and 0 on the right; positive
133. To rent a bike, the cost is $15 for the bike and $4 for each hour you bike. Draw a graph to represent the total cost of renting a bike.
y = 15 + 4x
134. A bacteria population starts with 20 bacteria and doubles every hour. Draw a function that represents the growth of the bacteria population over hours.
y = 20(2)^{x}
F.BF.1, 2: Build a function that models a relationship between 2 quantities
135. John already has $22 saved. He saves $5 each week so that he can buy a stereo. Write a function to model how much money John will save for x amount of weeks.
y = 22 + 5x
136. Billy has $1000 in his savings right now. He will withdraw 1/3 of his money each week. Write a function to model this situation.
y = 1000(1/3)^{x}
137. The terms of a given sequence increase by a constant amount. If the first term is 3 and the fourth term is 3:
a) List the first 6 terms in the sequence.
3, 1, 1, 3, 5, 7
b) What is the explicit formula for the sequence?
2n  5
c) What is the recursive formula for the sequence?
a_{n} = a_{n – 1} + 2; a_{1} = 3
138. The function f(n) = 2n + 5, create a table for the first 5 terms and identify the domain and range.
domain {1, 2, 3, 4, 5} range {3, 1 1, 3, 5}
139. Which function represents this sequence?
n

1

2

3

4

…

a_{n}

4

12

36

108

…

a. f(n) = 4^{n – 1} b) f(n) = 3^{n – 1} c) f(n) = 4(3)^{n – 1} d) f(n) = 3(4)^{n – 1}
140. Which function represents this sequence?
a

1

2

3

4

…

a_{n}

96

24

6

1.5

…

a_{n} = 96(1/4)^{n  1}
141. The first term in the sequence is 2. Which function represents the sequence?
a

1

2

3

4

…

a_{n}

2

8

14

20

…

a_{n} = 6n  4
142. The first term in the sequence is 4. Which function represents the sequence?
a

1

2

3

4

…

a_{n}

4

5

14

23

…

a_{n} = 9n  13
143. The points (0, 1), (2, 16), and (3, 64) are on the graph of a function. Which equation represents the function?
a. f(x) = 2^{x} b. f(x) = 3^{x} c. f(x) = 4^{x} d. f(x) = 5^{x}
144. The points (0, 1), (2, ¼), and (3, 1/8) are on the graph of a function. What equation represents the function? (1/2)^{x}
145. Use the graph to answer the questions.
a) Describe the behavior of the function within the interval ∞ to x = 1.
increasing
b) Describe the behavior of the function between the interval x = 1 to x = 1.
decreasing
c) Describe the behavior of the function from x = 1 to ∞
increasing
F.BF.3: Build New Functions from Existing Functions
146. If f(x) = 2x, how will g(x) = f(x) + 4 compare? How will h(x) = f(x) – 2 compare?
up 4; down 2
147. If f(x) = 3^{x}, how will f(x) + 1 compare? How will f(x) – 5 compare?
up 1; down 5
148. If f(x) = 2^{x}, how will g(x) = 2f(x) compare? How will h(x) 0.2f(x) compare? How will j(x) = f(x) compare?
vertical stretch; vertical shrink; reflection over xaxis
149. Suppose f is an even function and the point (3, 10) is on the graph of f. Name one other point that must be on the graph of f.
(3, 10)
150. Suppose f is an odd function and the point (3, 10) is on the graph of f. Name one other point that must be on the graph of f.
(3, 10)
151. Suppose f is an even function and the point (2, 4) is on the graph of f. Name one other point that must be on the graph of f.
(2, 4)
152. Suppose f is an odd function and the point (2, 4) is on the graph of f. Name one other point that must be on the graph of f.
(2, 4)
153. For the function f(x) = 4^{x}
a) Write the function that represents a 6 unit translation upward of f(x). 4^{x} + 6
b) Write the function that represents a 2 unit translation right of f(x). 4^{x  2}
c) Write a function that represents a reflection over the xaxis of f(x). 4^{x}
d) Is the function even, odd, or neiher? neither
154. Given the function f(x) = 2x + 1,
a) Describe what has happened if g(x) = 6x + 3 (or 3f(x)) vertical stretch by 3
b) Compare the function to f(4x). vertical stretch by 4 (steeper)
c) What has happened if g(x) = 2x + 1 reflect over xaxis or yaxis
d) Which has the fastest growth rate: f(x), 3f(x), or –f(x)? 3f(x) because it’s steeper
155. If you are given the function f(x) = 4, is it even, odd, or neither?
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