Name: _____________________________________
Chapter #4: Functions
Period: _____________
Date: ______________
Homework Packet #8
Days 1 – 5
COMPLETE THE FOLLOWING IN PENCIL ONLY. After completing the assignment, use the answer key
and a COLORED PEN to correct your work. Use your notes to help you answer the following. Answers are
provided.
#1 Intro to Functions
In each of the following examples, use an input-output chart to decide if the following relation is a
function. If your answer is NO, explain why.
1. Consider the following relation: multiply the
input by five and then subtract seven to get the
output.
2. Consider the following table;
3. Consider the following graph
4. Consider the following graph
1
For questions #5-9 use the graph below. Charlene heads out to school by foot on a fine spring day. Her
distance from school, in blocks, is given as a function of the time, in minutes, she has been walking. This
function is represented by the graph below.
5. How far does Charlene start off from school?
6. What is her distance from school after she has
been walking for 4 minutes?
7. After walking for six minutes, Charlene stops to
look for her subway pass. How long does she
stop for?
8. Charlene then walks to a subway station before
heading to school on the subway. How many
blocks did she walk to the subway?
9. How long did it take for her to get to school once she got on the train?
2
#2 Function Review Activity
Determine whether each relation is a function. Explain.
1.
2.
3.
4.
5.
6.
7. {(6, -1), (-4, 2), (5, 2), (4, 6), (6, 5)}
8.
9. {(2, 5), (4, -2), (3, 3), (5, 4), (-2, 5)}
10. 𝑥 = −3
11. 𝑦 = 𝑥 2 − 2
3
MIXED REVIEW:
Andrew has a new job at the local pizza store as a delivery boy. The following graph shows one of his deliveries
he made. Analyze the graph and answer questions #12-15.
12. How long was the entire trip?
13. If he arrived at the house after 4 minutes, how
far away was the house from the pizza place?
14. Why might Andrew have stopped 3 times for 1
minute?
15. Was Andrew’s trip longer going to the house or
coming back?
16. Determine whether each number is a solution of
√ 𝑥 + 2 ≥ 2.
a) 2
b) -1
17. Determine whether each number is a solution of
𝑥 2 + 3𝑥 = 18.
a) 3
b) -3
4
#3 Function Notation, Day 1
Questions #1-4: Given the function f defined by the formula f (x) = 2x + 1, find the following:
1. f (4)
2. f (-5)
1
4. 𝑓 (2)
3. f (0)
𝑥
5. MULTIPLE CHOICE: If the function f (x) is defined by f(x) = 2 − 6, then which of the following is the
value of f (10)? Show all of your work!
a. -1
b. 2
c. 14
d. 7
3
6. MULTIPLE CHOICE: If the function f (x) = 2x – 3 and g (x) = 2 𝑥 + 1 then which of the following is a
true statement? Show all of your work!
a. 𝑓(0) > 𝑔(0)
b. 𝑓(2) = 𝑔(2)
c. 𝑓(8) = 𝑔(8)
d. 𝑔(4) < 𝑓(4)
5
MIXED REVIEW:
7. Consider the function f (x) = 3(2 - x) – 2. Fill out the function table below for the inputs given and graph
the function on the axes provided. Make sure you label your function.
Determine whether each relation is a function. Explain.
8.
9.
Solve each equation for y.
10. y + 4x = 8
11. 2y = 8x
12. 3y + 6x = 12
6
#4 Function Notation, Day 2
Questions #1-5: If 𝒇(𝒙) = 𝒙𝟐 + 𝟓𝒙 − 𝟐𝟒 𝒂𝒏𝒅 𝒈(𝒙) = 𝒙𝟐 − 𝟒.
1. Find f (-3)
2. Find f (m)
4. g (a) + 9
5. f (2) + g (-2)
3. Find g (5)
Questions #6-10: If 𝒇(𝒙) = −𝟐𝒙 − 𝟑 𝒂𝒏𝒅 𝒈(𝒙) = 𝒙𝟐 + 𝟓𝒙.
6. Find g (-3)
9. g (a) + 9
7. Find 5[f (d)]
8. Find g (-6m)
10. f (2) + g (-2)
7
MIXED REVIEW:
Questions #11-14: Given the function g defined by the formula g (x) =
11. g (9)
12. g (0)
13. g (3)
14. g (17)
𝑥−5
2
, find the following:
Questions #15-18: Given the function f defined by the formula f (x) = 𝑥 2 − 4, find the following:
15. f (3)
1
17. 𝑓 (4)
16. f (-4)
18. f (-2)
8
#5 Illustrating Function Notation with a table/graph
1. Jenna knits scarves and then sells them on Etsy, an online marketplace. Let C(x) = 4x + 20 represent the cost
C in dollars to produce from 1 to 6 scarves. Fill in the table to show the relationship between the number of
scarves x and the cost C.
x, Number of
Scarves
Show work
here
C(x), Cost in
dollars
4. If the pattern continues, find the number of
scarves such that C(x) = 80.
2. For what value of x is C(x) = 28?
3. For what value of x is C(x) = 40?
5. From the table below list two possible solutions to the equation f(x) = 0.
Use the function shown in the table to answer the following.
x
1
2
3
4
f(x)
1
4
9
16
8. If f(x) = 4, then x = _________
6. f (3) = _________
7. f (4) = __________
9. If f(x) = 16, then x = ___________
9
Based on the graph of the function 𝑦 = 𝑔(𝑥) shown below, answer the following questions.
Evaluate each of the following and illustrate with a point on the graph.
10. 𝑔(−2) = ________
11. 𝑔(0) = _________
12. 𝑔(3) = _________
13. 𝑔(7) = _________
14. What value of x solves the equation 𝑔(𝑥) = 0 . These are called the zeroes of the function.
15. How many values of x solve the equation 𝑔(𝑥) = 2? How can you illustrate your answer on the graph?
Remember, we are not looking for exact x-values, only how many solutions.
MIXED REVIEW:
16. If f(x) = x2 – 3x + 8, evaluate f(-3).
−𝒃+√𝒃𝟐 −𝟒𝒂𝒄
17. Evaluate
𝟐𝒂
to the nearest tenth.
when a = 2, b = -8, c = -1
18. Solve, graph, write the solution set in interval notation: |2x – 3| < 5
10
Homework Packet #8 Answers:
#5 Illustrating Function
Notation
#1 Intro to Functions
#3 Function Notation Day 1
1. -22, -7, 23; yes
1. 9
2. no
2. -9
3. 3, 1, 4; yes
3. 1
2. 2
4. 1, 2, 3, 4, and 8; no
4. 2
3. 5
5. 22 blocks
5. A
4. 15
6. 14 blocks
6. C
7. 3 minutes
7. (-2, 10), (-1, 7), (0, 4),
8. 2 blocks
9. 4 minutes
(1, 1), (2, -2); correct graph
8. yes, provide explanation
1. See table at bottom of page
5. 𝑥 = √2 or 𝑥 = 𝜋
6. 9
7. 16
9. no, provide explanation
8. 2
10. y = -4x + 8
9. 4
1. yes, provide explanation
11. y = 4x
10. -3, put dot on graph
2. no, provide explanation
12. y = -2x + 4
11. -3, put dot on graph
#2 Function Review Activity
3. yes, provide explanation
4. no, provide explanation
5. no, provide explanation
6. yes, provide explanation
7. no, provide explanation
8. no, provide explanation
9. yes, provide explanation
10. no, provide explanation
11. yes, provide explanation
12. 15 minutes
13. 9 blocks
14. red lights
15. coming back
16. a) yes b) no
17. a) yes b) no
12. 4, put dot on graph
#4 Function Notation Day 2
1. -30
2. 𝑚2 + 5𝑚 − 24
3. 21
4. a2 + 5
5. -10
6. -6
7. -10d – 15
8. 36m2 – 30m
9. a2 + 5a + 9
10. -13
11. 2
12. -2.5
13. -1
14. 6
15. 5
16. 12
63
17. − 16 or -3.9375
18. 0
13. 0, put dot on graph
14. x = -3, 1, 5, and 7
15. 4, explain how you can
illustrate it on the graph.
16. 26
17. 4.1
18. correct graph; (-1, 4)
11
12