Linear functions: Domain & Range

Linear Functions:
Domain and Range

Students will be able to:

● A.2(A) determine the domain and range of a linear function in mathematical problems: determine reasonable domain and range values for real-world situations, both continuous and
discrete; and represent domain and range using
inequalities

Domain:
●

All possible input values
(x-values on the x-axis)

●

Independent variable

A quantity that is being
manipulated.

Domain and Range

Range:
●

All possible output values
(y-values on the y-axis)

●

Dependent variable

A quantity whose value depends on how the independent variable is manipulated

Independent variable: Number of miles ran
Dependent variable: Calories burnt

Multiple Choice

Mikaela is performing an experiment in she tracks the performance of a group of students and how long they studied. Which is the independent variable?

• The test scores

• The amount of time studied

Take 2-3 minutes to explore the
function machine on the next slide!

Function machine

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Spend 3 minutes discussing the
following with a partner:

●Explain what happens when you let x-values “flow” through the function machine.

●Which values are in the domain?

●Which values are in the range?

●How did modifying the linear function affect the range? Domain?

Discrete vs. Continuous Data

Discrete (can be counted)

Continuous (can be measured)

Multiple Choice

Determine if the following situation is discrete or continuous: the weights of newborn babies

• discrete
• continuous

Multiple Choice

Determine if the following situation is discrete or continuous: the number of days that students rode bikes to school

• Continuous
• Discrete

Inequalities

“Less than” x <

Example:
x < 5
“All x less than 5”

“Greater than” x >

Example:
x > 5
“All x greater than 5”

“Less than OR equal to” x ≤

Example:

x ≤ 5
“All x less than or equal to 5”

“Greater than OR equal to” x ≥

Example:
x ≥ 5
“All x greater than or equal to 5”

Discrete vs. Continuous

Discrete

A set of values consisting of only CERTAIN numbers in an
interval

Continuous

A set of values consisting of ALL numbers in an interval

Example:
Domain is {1, 2, 3, 34}
Only 1, 2, 3, and 34 are in
the domain

Example:
Range is 0 < y ≤ 34
All y values greater than
zero and less than OR
equal to 34

Open Ended

Describe what values are in this domain: 2 ≤ x < 10 

Draw

Circle your answer

Open Ended

Explain your thinking

Discrete vs. Continuous Graphs

You can draw a continuous
function without lifting your
pencil from your paper

A discrete graph is a
series of unconnected
points called a scatter plot.

Multiple Choice

Determine the domain of the graph

• The domain of the graph is all real numbers

• The domain of the graph is all x-values greater than or equal to 0 and less than or equal to 3

• The domain of the graph is {0, 1, 2, 3}

• The domain of the graph is {0, 3, 6, 9}

Domain and Range: Continuous Linear Functions

Use an open circle
for “less than” or
“greater than”

Use a closed circle for
“less than or equal to”
or
“greater than
or equal to”

Draw

Circle your answer

Open Ended

Explain your thinking

Poll

How do you feel today's lesson went?

To Do: Complete the homework assignment posted on google classroom