Domain and Range of Functions
Presentation
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Medium
+1
Standards-aligned
Danish Rehman
Used 12+ times
FREE Resource
15 Slides • 13 Questions
1
Multiple Choice
The student council sent its members on four field trips during the school year. The number of buses needed to transport the members on each trip is a function of the number of members who went on each trip. This function consists only the ordered pairs (52, 3), (72, 4), (86, 5), and (105, 6). What is the domain for this situation?
{52, 105}
{3, 4, 5, 6}
{52, 72, 86, 105}
{3, 4, 5, 6, 52, 72, 86, 105}
2
Multiple Choice
R: {0, 1, 2, -4}
R:{-4, -3, 1}
R:{1, -3, -4}
R: {1, -3, -4, 1}
3
A "relation" is a pairing of input values with output values.
The set of input values is called the domain and the set of output values is called the range.
4
Find the domain and range of this relation
5
For every function, there is only one y-value per x-value (or, one output per input). So,
if you can plug in an
input and get two
different answers,
then the relation is
not a function.
6
We can identify functions one of two ways: checking if any x-value has two or more
y-values, or using the
vertical line test on
relation graphs.
In the vertical line test,
if you draw a vertical
line through the graph
and hit two points on the graph, then it is not a function.
7
Is the above relation a function?
8
Multiple Choice
Identify the domain of the relation.
-9, -5, 1, 7
1, 4, 5, 8
-9, -5, 1, 1, 7
4, 8
9
An equation in two variables can relate two values like in the equation: y = 2x + 3. The input variable, x, is the independent variable and the output value, y, is the dependent variable (since its value depends on the value of the input).
10
To graph an equation in two variables, we select values for x, plug them in to the equation, and then solve for y. This gives us a coordinate pair (x, y) that we can plot on a Cartesian plane.
The relation to the right is a function and is linear.
NOTE: When working with functions, we sometimes use function notation which is written f(x) = mx + b, and f(x) stands in place of y.
11
Functions which contain variables with exponents are not linear.
Examples: y = 4x3 - 8, and y = 2x2 + 4x - 16 are not linear since one x-value in each has an exponent attached to it.
12
Domain (left to right)
Range (bottom to top)
13
14
Multiple Choice
Which algebraic notation represents the DOMAIN?
[−3,1]
−3<x≤1
(−3,1)
−3≤x<1
15
16
Multiple Choice
Which interval notation represents the Range?
[−2,4]
−2≤y≤4
(−2,4)
−2≤y<4
17
18
19
Multiple Choice
Which is the correct DOMAIN interval notation?
(-2,4]
[-2,4)
−2<x≤4
−2≤x<4
20
Multiple Choice
Which is the correct RANGE algebraic notation?
−2≤y≤3
[−2,3]
[−5,3]
−5≤y≤3
21
22
Multiple Choice
What is the DOMAIN of the graph?
y≥−3
[−∞,∞]
(−∞,∞)
23
Multiple Choice
What is the RANGE of the graph?
y≥−3
[−∞,∞]
(−∞,∞)
[∞,3]
24
Multiple Choice
The amount of money that Li spends on video games depends on how many games he purchases. If Li has at most $90 to spend on games for his Xbox 360 and the games cost $22.50 each, what is the domain of this function?
0≤x≤90
0≤x≤4
{0,1,2,3,4}
25
Multiple Choice
Thomas opened a savings account with $250. He plans to add $200 each week over the 12 week summer break. He will close the account at the end of summer. Which is an appropriate DOMAIN?
x≥0
0≤x≤2650
0≤x≤12
250≤x≤2650
26
Multiple Choice
Thomas opened a savings account with $250. He plans to add $200 each week over the 12 week summer break. He will close the account at the end of summer. Which is an appropriate RANGE?
y≥0
0≤y≤2650
0≤y≤12
250≤y≤2650
27
Multiple Choice
Which is the correct domain of the graph provided?
(−∞,−1)U(2,∞)
(−∞,−1]U[2,∞)
(−∞,∞)
28
The student council sent its members on four field trips during the school year. The number of buses needed to transport the members on each trip is a function of the number of members who went on each trip. This function consists only the ordered pairs (52, 3), (72, 4), (86, 5), and (105, 6). What is the domain for this situation?
{52, 105}
{3, 4, 5, 6}
{52, 72, 86, 105}
{3, 4, 5, 6, 52, 72, 86, 105}
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MULTIPLE CHOICE
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