Linear Functions REVIEW
Linear Functions
Algebra 1:
I. F.IF.2 Learning Target: Use function notation,
evaluate functions for inputs in their domains, and
interpret statements that use function notation in
terms of a context.
Name _____________________________________
Period _______________ Date _______________
3. Determine whether the graph represents a
function.
1. Determine whether the graph represents a
function. Then determine the domain and range.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
Function? ____________
–5
Explain your reasoning: __________________
Function? ____________
______________________________________
Explain your reasoning: __________________
Domain: _______________________________
______________________________________
Range: ________________________________
Domain: _______________________________
Range: ________________________________
4. Which of the following represents a function?
I
2. Which of the following relations is NOT a
function?
A.  2,1 ,  4,3 ,  6,5 , 8, 7 
Input
Output
1
2
3
4
1
1
1
1
II
Input
Outpu
t
10
9
8
9
4
5
6
7
III
Input
Outpu
t
5
6
7
8
3
4
2
2
B.  2,1 ,  4,3 ,  6,5 , 8,5
A. All
C.  2,1 ,  4,3 ,  6,5 ,  2, 7 
B. I and II
D.  2,1 ,  4,1 ,  6,5 , 8, 7 
C. I and III
D. II and III
Algebra 1: Linear Functions Unit Review
5/29/14
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5. Determine whether the graph represents a
function.
6. Emily has 36 doughnuts for Teacher
Appreciation Day. In addition, she is planning
on buying more boxes of doughnuts that contain
12 doughnuts each, if needed. All of the boxes
cost the same. Emily is not sure yet about the
number of boxes she wants to buy, but she has
enough money to buy up to 6 of them. Write a
function to describe how many doughnuts
Emily can possibly have available. Let x
represent the number of boxes Emily buys.
Find a reasonable domain and range for the
function.
Function: _____________________________
Domain: ______________________________
Range: _______________________________
II. A.REI.10 Learning Target: I can
understand that every point on the line
represents a solution to the linear equation.
Is this a function? YES or NO
7. Which point is a solution to 5 x  4 y  2 .
Explain your reasoning:______________________
_________________________________________
1
2




1
2
A.  , 0 


1
2
C.  0, 
________________________________________
B.  0,  
State the Domain:__________________________
 1
 2


D.   , 0 
State the Range: ___________________________
Evaluate f(5) _________
What is the meaning of f(5) in this scenario? Use
correct units.
Algebra 1: Linear Functions Unit Review
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8. Use the graph of the function f ( x)   x  2 to
answer the question that follow.
10. If a coordinate pair (x, y) makes the equation
NOT true, which of the following
statements is true?
A.A. The point (x, y) is not on the graph of
.
y
6
5
4
B. The point (x, y) is on the graph of
.
3
2
1
–6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
x
C. These values of x and y are the only ones
that satisfy
.
–2
–3
–4
–5
D. The coordinate pair (2x, 2y) also makes
the equation true.
–6
Part A: What is the value of f (2) ?
Part B: How many solutions does this function
have?
9. The function y  65 x describes how far from
home Jose is as he drives from San Francisco to
Dawson. Graph the function. Use the graph to
answer following
y
2000
1800
1600
Miles
1400
1200
1000
800
600
400
200
4
8
12
16
20
24
28
32
x
Hours
What is the value of f(18)?___________________
What is the meaning of f(18) in the context of the
problem?
_________________________________________
Algebra 1: Linear Functions Unit Review
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III. F.IF.4 Learning Target: For a linear function
that models the relationship between two quantities, I
can interpret the slope and the y-intercept.
13. Graph the line described by the equation
x  6 y  18 and identify the x and y intercepts.
11. What is the slope and y-intercept of the linear
function below?
x-intercept: __________
Slope: _________
y-intercept: _________
y-intercept: _________
12. Don opened a savings account with $300. Each
month, he will add $50 to the account. Let y
represent the amount of money in the account after
x months. Write an equation to model this
situation. What do the slope and y-intercept
mean in this situation?
14. Graph and state the slope, y-intercept and xintercept of the equation 2 x  4 y  12 .
Equation: ______________________________
Meaning: ______________________________
_______________________________________
_______________________________________
_______________________________________
Slope: ___________________
y-intercept: ______________
x-intercept: ______________
Algebra 1: Linear Functions Unit Review
5/29/14
PUHSD Curriculum Team
15. What is the slope, y-intercept and x-intercept of
the following function?
16. What are the y-intercepts of the functions?
Function A
x
y
0
15
5
5
10
-5
15
-15
Function B
f ( x)  15 x  13
Y-intercept of Function A: ___________
Y-intercept of Function B: _____________
Slope: ___________________
y-intercept: ______________
17. What are the slopes of the functions?
x-intercept: ______________
Function A
x
y
0
1
1
4
2
7
Function B
f ( x)   x  2
slope of Function A: ___________________
slope of Function B: ___________________
Algebra 1: Linear Functions Unit Review
5/29/14
PUHSD Curriculum Team
3
10
18. When Aidan had his picture taken, the
photographer charged a $10 sitting fee and $6
for each sheet of pictures purchased.
Part C: In this context what does the slope
represent?
Part A: Write a function for the situation, where x
is the number of sheets purchased.
Part D: What is the y-intercept of the table?
Part B: Explain how to find the cost of pictures if
Aidan bought 10 sheets of pictures. How
could you use the function to check this
answer?
19. The cost of a prepaid cell phone plan from
Cricket includes an activation fee plus a cost per
minute. The total costs are represented in the
table below.
Part E: What is the y-intercept of the function?
Part F: In this context what does the y-intercept
represent?
Cricket
Minutes Used (t) Total Cost f(t)
0
$7.50
1
$7.55
2
$7.60
3
$7.65
4
$7.70
Part G: Which company has a higher activation
fee? Explain your reasoning.
T-Mobile also charges an activation fee plus a rate
per minute. The total cost for T-Mobile’s plan when
t minutes are used is given by g (t )  10  0.10t .
Part A: What is the rate of change of the table?
Part H: Which company’s rate of change is higher?
Explain your reasoning.
Part B: What is the rate of change of the function?
Algebra 1: Linear Functions Unit Review
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PUHSD Curriculum Team
IV. F-BF.3 Learning Target: I can infer how
the change of the parameters m and b of
y=mx+b transform the graph.
20. Describe the transformation of the graph of the
1
function f ( x)  x  2 to the function
2
g ( x)  5 x  9 ?
V.
F.IF.7b Learning Target: Graph absolute
value functions expressed symbolically and show
key features of the graph, by hand in simple
cases and using technology for the more
complicated cases.
22. Given the absolute value function g ( x)  3 x  5
Part A: Graph the function on the graph below
21. The equation y  2 x  1 is graphed below.
How would the graph be affected if the
function were changed to y  2 x  5 .
Part B: Identify the vertex__________
23. The front of a camping tent can be modeled by
the function y  1.4 x  3  4 where the x and y
axis are measured in feet.
Part A: What parameter changed?
a.
b.
c.
d.
Using technology, find the maximum height of the
tent: __________________
slope
y-intercept
slope and y-intercept
neither
Part B: Describe the transformation.
Algebra 1: Linear Functions Unit Review
5/29/14
PUHSD Curriculum Team