Graphing Linear Functions-Target B: Justify whether any given representation is a function.

Situational Example
Your teacher wants to make a list of everyone's birthday months. She plans to make a two-column chart: one column will list the months of the year, and the other column is where she will fill in student's names.

a) How many options does she have to create the two-column chart?

The teacher has two options to create the chart. They can have the first column be the months of the year, and the second column can have the student names. Or the teacher can have the first column be the student names, and the second column have the months of the year.

b) What information in this situation represents the inputs?

It depends on how the teacher creates the two-colum chart. If the teacher lists the months first, then the months represent the inputs. If the teacher lists the names first, then the student names will represent the inputs.

c) If your teacher wants to create a function for this information, what would have to represent the inputs and outputs? Why?

The teacher would need to have the student names representing the inputs, and the month of the year representing the ouputs.

In option 1, the inputs (months) are paired with more than one output (students), causing this table to not repesent a function. In option 2, although there are multiple inputs paired with the same output, there are no repeating inputs, so this table IS representing a function.

1) Could the following situation represent a function? Pairing the town students live in with the school they attend.
a) Yes: If the towns represent the x-values and the schools represent the y-values.
b) Yes: If the schools represent the x-values and the towns represent the y-values.
c) A function cannot be represented from this situation.

2) Determine the domain and range in order for a game of bowling to represent a function.
a) Frames would represent the domain; number of pins would represent the range.
b) Number of pins would represent the domain; frames would represent the range.
c) A function cannot be represented from this situation.

3) Can the following situation be represented as a function? A teacher pairs students with their grades on an assessment.
a) Yes: If the grades represent the inputs and the students represent the outputs.
b) Yes: If the students represent the inputs and the grades represent the outputs.
c) A function cannot be represented from this situation.

## Graphing Linear Functions-Target B: Justify whether any given representation is a function.

Situational ExampleYour teacher wants to make a list of everyone's birthday months. She plans to make a two-column chart: one column will list the months of the year, and the other column is where she will fill in student's names.

a) How many options does she have to create the two-column chart?

The teacher has two options to create the chart. They can have the first column be the months of the year, and the second column can have the student names. Or the teacher can have the first column be the student names, and the second column have the months of the year.

b) What information in this situation represents the inputs?

It depends on how the teacher creates the two-colum chart. If the teacher lists the months first, then the months represent the inputs. If the teacher lists the names first, then the student names will represent the inputs.

c) If your teacher wants to create a function for this information, what would have to represent the inputs and outputs? Why?

The teacher would need to have the student names representing the inputs, and the month of the year representing the ouputs.

In option 1, the inputs (months) are paired with more than one output (students), causing this table to not repesent a function. In option 2, although there are multiple inputs paired with the same output, there are no repeating inputs, so this table IS representing a function.

## Quick Check - Context Functions Situations

1) Could the following situation represent a function? Pairing the town students live in with the school they attend.

a) Yes: If the towns represent the x-values and the schools represent the y-values.

b) Yes: If the schools represent the x-values and the towns represent the y-values.

c) A function cannot be represented from this situation.

2) Determine the domain and range in order for a game of bowling to represent a function.

a) Frames would represent the domain; number of pins would represent the range.

b) Number of pins would represent the domain; frames would represent the range.

c) A function cannot be represented from this situation.

3) Can the following situation be represented as a function? A teacher pairs students with their grades on an assessment.

a) Yes: If the grades represent the inputs and the students represent the outputs.

b) Yes: If the students represent the inputs and the grades represent the outputs.

c) A function cannot be represented from this situation.

To see explanations from the quick check, click on the link below:

Quick Check Solutions - Context

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