domain and range

Domain and Range

​Please have out your notebook for guided notes:

Agenda: We will analyze input and output values from a graph related to real-world problems.

I will identify the domain and range from real-world situations.

​Domain- (x) input values.

​The domain of a function is the set of input values or all possible x-values listed least to greatest (left to right on a graph). There are two types of graphs you can have. (discrete and continuous)

​discrete continuous

Multiple Choice

What values are associated with domain?

• x - input

• y - output

The domain of this graph is all the (x) values of each point.

*remember, each coordinate is (x,y) so, for domain you are looking at the first number inside each parenthesis. You always look from left to right.

​

This graph is discrete because it has points instead of a line segment.

Fill in the Blanks

please fill out the missing domain value. *hint, look at the x values of each point*

{ -4, -2,

, 3}

The domain of this graph is all the (x) values of each point.

think of where each dot would "fall" into the x axis.

This example this graph would have a domain of {0, 1, 2, 3, 4, 5, 6}

​

This graph is discrete because it has points instead of a line segment.

Multiple Choice

What is the domain for the image shown?

• all real numbers

• {1, 2, 3, 4, 5}

• {0, 1, 2, 3, 4, 5}

Drag and Drop

What is the domain of the function shown?​

Placeholder

Drag these tiles and drop them in the correct blank above

{1, 2, 3, 4, 5, 6,7, 8 }

{0, 1, 2, 3, 4, 5, 6, 7, 8}

{5, 10, 15, 20, 25, 30, 35, 40}

Continuous graphs have a subset of the domain or range of the full function including a lower and upper boundary. They are written in inequality notation.

​Continuous Graphs

To find the domain of a continuous graph use the most left and most right dot and think where would the dot "crash" into the x axis.

​Continuous Graphs

To write the domain on continous graphs use inequality notation. Open dots use </> and closed use ≤/≥.

the left value goes first, the right value second!

​Continuous Graphs
"Inequality notation"

Remember for every coordinate it is (x,y), domain is x values, so only look at the first number of every coordinate.

For this example the answer would read as follows.

− 3 < x ≤ 6.

Multiple Choice

What is the domain inequality notation for the graph shown?

• − 2 < x < 6

• − 3 < x ≤ 6.

• -3 < x < 6

• 6 < -3

Multiple Choice

What is the domain inequality notation for the graph shown? *remember to look if the dot is open or closed!

• -5 < x < 5,

• -5 ≤ x ≤ 5

• -5 < x ≤ 5

Multiple Choice

What is the domain inequality notation for the graph shown? *remember to look if the dot is open or closed!

• -9 ≤ x < 2

• -6 ≤ y < 3

• -9 < x ≤ 2

• -6 < y ≤ 3

Multiple Choice

What is the domain inequality notation for the graph shown? *remember to look if the dot is open or closed!

• 9 ≤ x < 0

• 9 ≤ x ≤ 28

• 0 ≤ x ≤ 28

​Range (y) - output values.

Range is the output values or all possible y-values also listed least to greatest. Range goes from bottom to top on a graph. You will be asked to find range with discrete and continuous graphs.

​discrete continuous

Multiple Choice

What values are associated with range?

• x values- input

• y values- output

The range of this graph is all the (y) values of each point.

*remember, each coordinate is (x,y) so, for range you are looking at the second number inside each parenthesis. You always look from bottom to top.

​

This graph is discrete because it has points instead of a line segment.

Fill in the Blanks

Fill out the missing range value. *hint, look at the y values of each point go from bottom to top*

{ -2, -1, 2,

}

The range of this graph is all the (y) values of each point.

think of where each dot would "run into" into the y axis.

This example this graph would have a range of {0, 30, 60, 90, 120, 150}

​

This graph is discrete because it has points instead of a line segment.

Drag and Drop

What is the range of the function shown?​

Placeholder

Drag these tiles and drop them in the correct blank above

{5, 10, 15, 20, 25, 30, 35, 40 }

{0, 1, 2, 3, 4, 5, 6, 7, 8}

{0, 5, 10, 15, 20, 25, 30, 35, 40}

To find the range of a continuous graph use the lowest and highest dot and think where would the dot "crash" into the y axis.

​Continuous Graphs

To write the range on continous graphs use inequality notation. Open dots use </> and closed use ≤/≥.

the bottom value goes first, the top value second!

​Continuous Graphs

Multiple Choice

What is the range inequality notation for the graph shown?

• − 2 < y < 6

• − 2 < y ≤ 6.

• -2 < y ≤ 1

• 6 < -3

Multiple Choice

What is the range inequality notation for the graph shown?

• -7 ≤ x < 3

• -5 < y ≤ 1

• 1 ≤ y < -5

• -6 < x ≤ 1

Multiple Choice

What is the range inequality for the graph shown?

• 1 ≤ y < 7

• -5 < y ≤ 1

• 7 < y ≤ 1