Domain and Range Using Set Notation

Functions​

Multiple Select

Which of the following can represent the x-values of a function

• Input

• Output

• Independent variable

• Dependent variable

• Domain

Multiple Select

Which of the following can represent the y-values of a function

• Input

• Output

• Independent variable

• Dependent variable

• Range

Domain and Range

​Domain

In mathematics, the domain of a function is the set of inputs accepted by the function.

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​We know that the input of a function is referring to the x-values

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​When talking about the domain you list all the x-values of a function is set notation

Range

In mathematics, the range of a function is the set of outputs values that are related to the input values

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​We know that the output of a function is referring to the y-values

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​When talking about the range you list all the y-values of a function is set notation

Set Notation

Set notation is using the symbols { and } all the values of the domain and range are listed inside of the brackets

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​If a value repeats in the domain and range you do not write it twice

Example #1

​Domain: {-8, -2, 0, 2 6}

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​Range: {0, 1, 4, 6}

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​Notice the value 4 repeated twice for y, but in the range it was only written once

Example #2

​Domain: {-5, -4, 1, 2, 3, 5}

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​Range: {-5, -4, -3, 0, 2}

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​Notice the value -3 repeated twice for y, but in the range it was only written once

Multiple Choice

What is the Domain of the function

• {-4, -2, 4, 5}

• {-5, -3, -1, 1, 2, 4}

• {-4, -2, 0, 1, 4, 5}

• {-5, -3, 1, 4}

Multiple Choice

What is the Range of the function

• {-4, -2, 4, 5}

• {-5, -3, -1, 1, 2, 4}

• {-4, -2, 0, 1, 4, 5}

• {-5, -3, 1, 4}

Multiple Choice

What is the Range of the function

• {-10, -7, -4, 2, 4, 5}

• {-7, -4, 4, 5}

• {-10, -7, 2, 5}

• {-10, 2, 5}

Multiple Choice

What is the Domain of the function

• {-10, -7, -4, 2, 4, 5}

• {-7, -4, 4, 5}

• {-10, -7, 2, 5}

• {-10, 2, 5}

Linear and Non-Linear

​Linear Functions: Graphs

​When a linear function is graphed, it will always create a straight line. It can be horizontal or slanted, but it will have no curves

​Non-Linear Functions: Graphs

​When a non-linear function is graphed, it will always have one or more curves in the graph

Multiple Select

Select ALL the linear functions

Multiple Select

Select ALL the non-linear functions

​Linear Functions: Equations

​Non-Linear Functions: Equations

Multiple Select

Select ALL linear function

• $$y=9x+7$$  

• $$y=\frac{5}{x}$$  

• $$y=x^2+3x$$  

• $$y=4^x+3$$  

• $$y=1$$  

Multiple Select

Select ALL non-linear function

• $$y=7x^5+2x^2-9$$  

• $$y=\frac{4}{x}-11$$  

• $$y=2x$$  

• $$y=4^x+3$$  

• $$y=\sqrt[]{x}+15$$  

Interpreting ​Points on a Graph

​Labels on a graph

​You will be given the graph of a function and it will be labeled as follows. Each label will identify what the function represents, as well as the x and y values.

Example #1

​If there are 30 guests, how much will Baldwin's birthday party cost?

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​First you are going to want to identify if guests are represented by the x or y values.

​Example #1

​Now that we know that guests is the x-values, we need to find the point on the graph that corresponds with the value.

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​That points will tell us our solution:

​If there are 30 guests, the cost of the party will be $300

​Example #2

​If there are $40 left to raise, how many cookies have been sold?

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First you are going to want to identify if money left to raise is represented by the x or y values.

​Example #2

​Now that we know that Money left to raise is the y-value, we need to find the point on the graph and the value that corresponds to it.

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​The point will tell us the solution:

​If there are $40 left to raise, then 50 cookies have been sold.