Functions: Domain and Range

Y can have more than one X.

X cannot have more than one Y.

5-Minute CheckWrite the domain and range of the relation. Then

determinewhether each relation is a function. x 4 1 3 6

y 2 3 3 4

5-Minute CheckWrite the domain and range of the relation. Then

determinewhether each relation is a function. x 4 1 3 6

y 2 3 3 4

D= {4,1,3,6}; R= {2,3,4}; yes

1)

5-Minute Check

{(4,2), (-3,2), (8,2), (8,9), (7,5)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

2)

5-Minute Check

{(4,2), (-3,2), (8,2), (8,9), (7,5)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

2)

5-Minute Check

{(4,2), (-3,2), (8,2), (8,9), (7,5)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

D={4,-3,8,7}; R= {2,9,5}; no

2)

5-Minute Check

{(-3,1), (0,2), (2,4)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

3)

5-Minute Check

{(-3,1), (0,2), (2,4)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

D={-3,0,2}; R= {1,2,4}; yes

3)

5-Minute Check

{(1,5), (1,3), (4,5)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

3)

5-Minute Check

{(1,5), (1,3), (4,5)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

D={1,4}; R= {5,3}; no

3)

5-Minute Check

{(5,6), (-3,0), (1,1), (-3,6)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

4)

5-Minute Check

{(5,6), (-3,0), (1,1), (-3,6)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

D={5,-3,1}; R= {6,0,1}; no

4)

5-Minute Check

{(4,2), (-3,2), (8,2), (8,9), (7,5)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

5)

5-Minute Check

{(4,2), (-3,2), (8,2), (8,9), (7,5)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

D={4,-3,8,7}; R= {2,9,5}; no

5)

5-Minute Check

{(1,3), (-3,5), (-2,5), (2,3)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

6)

5-Minute Check

{(1,3), (-3,5), (-2,5), (2,3)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

D={1,-3,-2,2}; R= {3,5}; yes

6)

5-Minute Check

{(3,-4), (1,0), (2,-2), (3,2)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

7)

5-Minute Check

{(3,-4), (1,0), (2,-2), (3,2)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

D={3,1,2}; R= {-4,0,-2,2}; no

7)

5-Minute Check

{(0,4), (-3,-2), (3,2), (5,1)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

8)

5-Minute Check

{(0,4), (-3,-2), (3,2), (5,1)}

Write the domain and range of the relation. Then determinewhether each relation is a function.

D={0,-3,3,5}; R= {4,-2,2,1};

8)

5-Minute CheckUse the scatter plot to answer each question.

3. What kind of relationship, if any, is shown by the scatter plot?

Weights and Heights of Basketball players

Weight (pounds)

Height

5-Minute CheckUse the scatter plot to answer each question.

3. What kind of relationship, if any, is shown by the scatter plot?

positive

Weights and Heights of Basketball players

Weight (pounds)

Height

5-Minute CheckUse 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?

Weights and Heights of Basketball players

Weight (pounds)

Height

5-Minute CheckUse 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, 6’2” player

Weights and Heights of Basketball players

Weight (pounds)

Height

Problem-Solving strategy - Draw a Graph

Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface.

Problem-Solving strategy - Draw a Graph

Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface.

Altitude(thousands of feet)

Temp(°F)

5 41

10 23

15 4

20 -15

25 -33

Problem-Solving strategy - Draw a Graph

Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface.

Altitude(thousands of feet)

Temp(°F)

5 41

10 23

15 4

20 -15

25 -33

The temperature at different altitudes above sea level when the temperature at sea level is 60°F is shown in the table at the left.

Problem-Solving strategy - Draw a Graph

Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface.

Altitude(thousands of feet)

Temp(°F)

5 41

10 23

15 4

20 -15

25 -33

The temperature at different altitudes above sea level when the temperature at sea level is 60°F 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?

Problem-Solving strategy - Draw a Graph

Imagine you are sitting in your summer clothes and sandals eating lunch and it’s 74 degrees below zero! It happens every day on high-flying airplanes that are far from the heat of Earth’s surface.

Altitude(thousands of feet)

Temp(°F)

5 41

10 23

15 4

20 -15

25 -33

The temperature at different altitudes above sea level when the temperature at sea level is 60°F 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

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.

Problem-Solving strategy - Draw a Graph

Assignment: 6 - 17 all.

Pages 398 & 399