Name: _____________________
Class: _________________
M8-U4: Function & Linear Relationships Review
Total: 50pts
Multiple Choice: Circle the letter/number that best answers each question below.
(2 pts each)
1. What is the equation of the line that passes through point 5,8 and has a y-intercept of -2?
a) y 
5
x2
2
b) y 
7
x2
2
c) y  2 x  2
d) y  6 x  2
2. Which table does not show the patterns of a linear relationship?
a)
x
-2
3
7
11
y
5
-5
-13
-21
b)
x
-3
-1
1
3
y
4
6
7
10
c)
x
-2
-1
0
1
y
-4
-1
2
5
d)
x
-2
0
2
4
y
10
20
30
40
3. The gas tank in a car holds a total of 16 gallons of gas. The car travels 75 miles on 4 gallons
of gas. If the gas tank is full at the beginning of a trip, which graph represents the rate of
change in the amount of gas in the tank?
1
4.
5.
Which diagram represents a function?
a)
b)
c)
d)
Based on the following two functions, which statement is correct?
Function A
x 1 3 4 6
Function B
y  4x  3
y 5 13 17 25
a) Function A has a greater rate of change than Function B.
b) Function B has a greater rate of change than Function A.
c) The rates of change are equal for both functions.
d) Function B has a negative rate of change while Function A is positive.
2
Short Answer: Answer the following questions completely. Show all of your work and
remember to label your answers.
6. Use the graph below. Describe the speed of a car over time.
(3 pts)
y
Speed (mi/h)
60
50
40
30
20
10
0
0
5
10
15
x
Time (s)
7. For each of the equations below find their slopes and y-intercepts.
(1 pt each)
3
x6
4
slope ____________
y-intercept ___________
b) y  7  2 x
slope ____________
y-intercept __________
a) y 
3
8.
(3 pts)
Given the following relations:
 5,1,  3,2, 0,3, 1,1, 2,0, 6,4, 8,2, 8,7
State the domain and range for the relation.
Professor Octavius said the relation above is also a function. Explain why Professor
Octavius is correct or incorrect.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
4
9.
What is the slope, y-intercept, and equation for the following graph?
(3 pts)
Slope: __________________
y-intercept: ________________
Equation: __________________
10.
What is the slope, y-intercept, and equation for the following graph?
(3 pts)
Slope: __________________
y-intercept: ________________
Equation: __________________
5
11.
Complete the table below with the missing values for y.
(3 pts)
x y
-4 14
-3 11
-2
8
-1
5
0
1
On the line below, write a function rule that shows the relationship between x and y in the
table.
Answer _______________________________________________________________
12.
A line contains the points (2, 1) and (4, 5). What is the equation of the line?
Must be solved algebraically.
Equation: _______________________________________
6
(3 pts)
13.
a) Graph the following equation: y  3 x  5 .
(3 pts)
y
8
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
x
–2
–3
–4
–5
–6
–7
–8
b) Is (4, -8) a solution to the above equation? Show or explain.
14.
Graph the following equation: y 
2
x.
3
(2 pts)
y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
7
15.
a) Graph the following equation: 3x  2 y  4 .
(3 pts)
y
8
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
x
–2
–3
–4
–5
–6
–7
–8
b) What is the slope and y-intercept of the graph above?
16.
The cost, C , of a car wash depends on the time you wash, t.
Suppose a car wash costs $1.50 per minute plus a $2 initial charge.
a) Write a function for the cost of a car wash.
b) Using the equation, what is the cost of a 14 minute car wash?
c) Using the equation, how long can you wash your car if you are charged $20?
8
(4 pts)
17.
Is the equation y 
4
linear or nonlinear? Show work or explain.
x
(3 pts)
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
18.
The graph shows the amount of water in a bath tub as a function of time.
(3 pts)
Calculate the rate of change. Explain what the rate of change and y-intercept means in
context to the situation.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
9