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Study guide/ practice
Unit 6 Test, “Functions”
Note: Many problems in this packet will be completed together in class during review
time. Students are not expected to complete every single problem in the packet. They
should complete the “starred” problems on each page-- in addition to studying the
notes and past quizzes– in order to be fully prepared for test.
Topics:
Vocabulary:
domain, range, independent, dependent, relation, function, slope, y-intercept
(see Quick Guide for definitions/ descriptions)
Identifying a function
Function tables (“magic #” shortcut)
Solving linear equations
Graphing linear equations (slope-intercept form– y = mx + b)
4 ways to represent a function (Equation, Words, Table, Graph)
Input
Output
On the back of this cover page is the Unit 6 “Quick Guide” – for your reference.
Unit 6, “Functions,” Quick Guide
ALWAYS try your BEST!!
Equation
y = 3x + 2
Plug in the “x”
values from
the table!
Table
x
y
-1
-1
0
2
1
5
2
8
Graph
All ordered
pairs must fit
on line!
Fill-in-the-Blanks:
A function is a special type of ______________________________________ where every member of the
domain is paired with exactly __________member of the range. In other words, there can never be
a repeating ______________________ value in the same relation.
1. Which of the following relations is not a function?
2. Which of the following relations is a function?
3. Which of the following is NOT a function?
4. Which of the following is a function?
5. Which of the following is NOT a function?
Write the linear equation that represents each of the following function tables:
1)
2)
x
y
0
-1
1
5
2
3
x
y
0
3)
x
y
3
-2
0
1
10
1
15
2
4)
x
y
-5
0
-1
-1
-2
1
1
-1
0
1
2
3
-3
1
4
3
5
y = ________________
y = ________________
y = ________________
y = ________________
5)
6)
7)
8)
x
y
4
-1
1
8
2
3
x
y
x
y
0
-3
-2
0
0
12
1
16
2
y = ________________
x
y
-5
0
6
-1
-1
1
4
3
0
3
2
2
6
1
7
3
0
y = ________________
y = ________________
y = ________________
Remember the shortcut: Find the pattern
going down “y” & use the “magic #” to
MULTIPLY to the “x” #!!
Which linear equation matches the following function tables?
1)
2)
3)
4)
x
-1
0
1
2
3
y
0
2
4
6
8
A)
y= x+1
B)
y= x+2
C)
y = 2x + 2
x
-2
-1
0
1
2
A)
y= x–3
y
11
8
5
2
-1
B)
y = -3x + 5
C)
y=
x+5
x
-2
0
2
4
6
A)
y= x–6
y
-8
0
8
16
24
B)
y= x+8
C)
y = 4x
x
3
6
9
12
15
A)
y= x+9
y
10
19
28
37
46
B)
y = 2x + 4
C)
y = 3x + 1
CAREFUL . . . Can you
use the shortcut for #3
and #4???
Solve the following linear equations (plug in “x” values exactly where “x” is in equation):
Equation
1)
Table
y=x–3
4)
x
2)
3)
Equation
y = -3x + 4
Table
y= -x+5
y
x
-1
-5
0
-3
1
15
2
20
x
y
5)
y = 4x - 6
x
-5
-4
-1
-2
0
0
5
2
x =y+6
6)
x
y
y
y
x = 2y – 4
x
-24
-4
-12
-1
0
0
12
3
y
It’s ok to have
fraction outputs!
Fill-in-the-Blanks:
There are _____________________________ ways to represent a function. We can use an equation,
words, a table, or a graph. If we are given one representation, we can use that information to find
the other three ways to represent the function.
Equation
Words
Table
Graph
1)
x
y
x
y
x
y
0
-3
1
0
2
3
3
6
x
y
y = 3x -2
2)
“y is equal to
twice a number,
minus four.”
3)
4)
6)
7)
8)
9)
10)
11)
12)
14)
15)
13)