Name: ______________________________Block: _____
Functions Study Guide SOLs 7.12 and 7.2
Functions
Vocabulary You Should Know:
•
•
•
•
•
•
•
•
•
•
•
•
Relation
Function
Domain
Range
Input
Output
Independent Variable
Dependent Variable
Linear Equation
Slope
Arithmetic Sequence
Geometric Sequence
Questions You Should Be Able to Answer:
1. In your own words, explain what makes a relation a function.
A relation is a function when every input (x-value) is paired with one
and only one output (y-value).
2. What three terms can we use to describe the set of all possible x-values?
Input, Domain, Independent Variable
3. What three terms can we use to describe the set of all possible y-values?
Output, Range, Dependent Variable
5. How do I find the slope of a line?
Calculate the change is y (rise) over the change in x (run). Simplify
your answer.
6. Find the slope each line graphed below:
-3
0
1/3
Name: ______________________________Block: _____
Functions Study Guide SOLs 7.12 and 7.2
7. Identify the domain and range of each relation.
Then, determine if the relation is a function.
A. {(-4, 3), (6, 2), (4, 5), (-6, 1)}
B. {(1, -5), (1, -6), (2,-7), (2, -8), (3, -9)}
Function
D: {-6, -4, 4, 6}
R: {1, 2, 3, 5}
Not a Function
D: {1, 2, 3}
R: {-9, -8, -7, -6, -5}
C.
x
y
2
D.
x
y
5
-2
6
-1
1
7
0
4
1
Not a Function
D: {2}
R: {5, 6, 7}
Function
D: {-2, -1, 0, 1}
R: {1, 4}
E .
F.
x
8
9
10
11
12
13
y
0
-1
-2
-3
-4
-5
Function
D: {8, 9, 10, 11, 12, 13}
R: {-5, -4, -3, -2, -1, 0}
x
4
3
2
1
0
-1
y
16
9
4
1
0
1
Function
D: {-1, 0, 1, 2, 3, 4}
R: {0, 1, 4, 9, 16}
Name: ______________________________Block: _____
Functions Study Guide SOLs 7.12 and 7.2
8. Create a table of values for the given equation. Use your table to graph the function.
A. y = 2x - 5
Use the domain {-2, -1, 0, 1, 2}.
-2
-1
0
1
2
B. y = -x - 2
Choose any four domain values.
-9
-7
-5
-3
-1
-1
0
1
2
-1
-2
-3
-4
C. 𝒚 = 𝟐 + 𝟑
Choose any four domain values.
𝒙
D. 𝒚 = −𝟑𝒙 + 𝟐
Choose any four domain values.
-2
2
-1
5
0
3
0
2
2
4
1
-1
4
5
2
-4
9. What is the slope of each of the lines above?
#9. ______2______ #10. ______-1_____ #11. ___1/2_______ #12. ___-3________
10. Are the functions graphed above linear? How do you know?
Yes. I know because every single graph is a line.
Name: ______________________________Block: _____
Functions Study Guide SOLs 7.12 and 7.2
11. Consider the sequences below.
a. State whether the sequence is arithmetic, geometric, or neither.
b. If applicable, identify the common difference or ratio.
A) 8, 3, -2, -7, ….
B) 1, 1, 2, 3, 5, …
Arithmetic
Neither
Common Difference: -5
C) 4, -8, 16, -32, ….
D) 5, 12.2, 19.4, 26.6 …
Geometric
Arithmetic
Common Ratio: -2
Common Difference: 7.2
12. Consider the geometric sequence 54, 18, 6, . . . .
What is the common ratio?
1/3
What will be the next term? ____2___
13. Consider the sequence 11, 9, 7, 5, . . . .
What will be the 8th, 9th, and 10th terms? __-3____ ___-5____ ___-7____
14. Consider the sequence 1, 2, 4, 8 . . .
a. Which term will be 128? __8th_____
b. Is it possible for 301 to be a term? Why or why not?
No. Every term in this sequence is a multiple of 2.
301 is not a multiple of two, so it cannot be in this sequence.