Functions: Domain and Range

1
Functions Domain and Range

• Y can have more than one X.
• X cannot have more than one Y.

2
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.

x 4 1 3 6
y 2 3 3 4
3
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.

1)
x 4 1 3 6
y 2 3 3 4
D 4,1,3,6 R 2,3,4 yes
4
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
2)
(4,2), (-3,2), (8,2), (8,9), (7,5)
5
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
2)
(4,2), (-3,2), (8,2), (8,9), (7,5)
6
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
2)
(4,2), (-3,2), (8,2), (8,9), (7,5)
D4,-3,8,7 R 2,9,5 no
7
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
3)
(-3,1), (0,2), (2,4)
8
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
3)
(-3,1), (0,2), (2,4)
D-3,0,2 R 1,2,4 yes
9
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
3)
(1,5), (1,3), (4,5)
10
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
3)
(1,5), (1,3), (4,5)
D1,4 R 5,3 no
11
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
4)
(5,6), (-3,0), (1,1), (-3,6)
12
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
4)
(5,6), (-3,0), (1,1), (-3,6)
D5,-3,1 R 6,0,1 no
13
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
5)
(4,2), (-3,2), (8,2), (8,9), (7,5)
14
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
5)
(4,2), (-3,2), (8,2), (8,9), (7,5)
D4,-3,8,7 R 2,9,5 no
15
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
6)
(1,3), (-3,5), (-2,5), (2,3)
16
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
6)
(1,3), (-3,5), (-2,5), (2,3)
D1,-3,-2,2 R 3,5 yes
17
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
7)
(3,-4), (1,0), (2,-2), (3,2)
18
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
7)
(3,-4), (1,0), (2,-2), (3,2)
D3,1,2 R -4,0,-2,2 no
19
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
8)
(0,4), (-3,-2), (3,2), (5,1)
20
5-Minute Check
Write the domain and range of the relation. Then
determine whether each relation is a function.
8)
(0,4), (-3,-2), (3,2), (5,1)
D0,-3,3,5 R 4,-2,2,1
21
5-Minute Check
Use the scatter plot to answer each question.
3. What kind of relationship, if any, is shown by
the scatter plot?
H e i g h t
Weight (pounds)
Weights and Heights of Basketball players
22
5-Minute Check
Use the scatter plot to answer each question.
3. What kind of relationship, if any, is shown by
the scatter plot? positive
H e i g h t
Weight (pounds)
Weights and Heights of Basketball players
23
5-Minute Check
Use the scatter plot to answer each question.
3. What kind of relationship, if any, is shown by
the scatter plot? positive 4. What does the point
with the triangle around it represent?
H e i g h t
Weight (pounds)
Weights and Heights of Basketball players
24
5-Minute Check
Use the scatter plot to answer each question.
3. What kind of relationship, if any, is shown by
the scatter plot? positive 4. What does the point
with the triangle around it represent? 185 pound,
62 player
H e i g h t
Weight (pounds)
Weights and Heights of Basketball players
25
Problem-Solving strategy - Draw a Graph
Imagine you are sitting in your summer clothes
and sandals eating lunch and its 74 degrees
below zero! It happens every day on high-flying
airplanes that are far from the heat of Earths
surface.
26
Problem-Solving strategy - Draw a Graph
Imagine you are sitting in your summer clothes
and sandals eating lunch and its 74 degrees
below zero! It happens every day on high-flying
airplanes that are far from the heat of Earths
surface.
Altitude (thousands of feet) Temp (F)
5 41
10 23
15 4
20 -15
25 -33
27
Problem-Solving strategy - Draw a Graph
Imagine you are sitting in your summer clothes
and sandals eating lunch and its 74 degrees
below zero! It happens every day on high-flying
airplanes that are far from the heat of Earths
surface.
The temperature at different altitudes above sea
level when the temperature at sea level is 60F
is shown in the table at the left.
Altitude (thousands of feet) Temp (F)
5 41
10 23
15 4
20 -15
25 -33
28
Problem-Solving strategy - Draw a Graph
Imagine you are sitting in your summer clothes
and sandals eating lunch and its 74 degrees
below zero! It happens every day on high-flying
airplanes that are far from the heat of Earths
surface.
The temperature at different altitudes above sea
level when the temperature at sea level is 60F
is shown in the table at the left. The table
does not include an altitude for 74. At what
altitude would a jet be flying when the
thermometer has this reading?
Altitude (thousands of feet) Temp (F)
5 41
10 23
15 4
20 -15
25 -33
29
Problem-Solving strategy - Draw a Graph
Imagine you are sitting in your summer clothes
and sandals eating lunch and its 74 degrees
below zero! It happens every day on high-flying
airplanes that are far from the heat of Earths
surface.
The temperature at different altitudes above sea
level when the temperature at sea level is 60F
is shown in the table at the left. The table
does not include an altitude for 74. At what
altitude would a jet be flying when the
thermometer has this reading? 36,000 feet
Altitude (thousands of feet) Temp (F)
5 41
10 23
15 4
20 -15
25 -33
30
Problem-Solving strategy - Draw a Graph
The ordered pairs (50.7, 16.47) and (99.92,
25.42) represent data from two rows of a table
comparing cubic meters of natural gas used and
the cost. What would the bill for 140 cubic
meters of natural gas be?
Plot the points and then draw a line through both
points. Find 140 on the graph and then follow it
to the corresponding cost.
31
Problem-Solving strategy - Draw a Graph
Assignment 6 - 17 all. Pages 398 399