Remember that a function is a type of relation for which there is exactly one output for each input.
Mapping Diagram:
Domain: {60,120,180,240} Range: {360,720,1080,1440} Interpretation of the Context: See solution. Relation: The relation is a function.
Practice makes perfect
We know that a person can burn about 6 calories per minute bicycling. If x represents the number of minutes bicycled, and y represents the number of calories burned, we can write a relation between x and y.
y= 6x
Now, let's make a table of values for the given time values.
x
Relation: y=6x
y
60
y=6( 60)
360
120
y=6( 120)
720
180
y=6( 180)
1080
240
y=6( 240)
1440
Mapping Diagram
Next, we will create a mapping diagram by using the values from the table.
Domain and Range
Let's determine the domain and the range of the relation. First, let's recall what the domain and range of a relation are.
The domain is the possible inputs of a relation.
The range is the possible outputs of a relation.
In this case, the number of minutes bicycled will be the domain and the number of calories burned will be the range.
Domain:& {60,120,180,240}
Range:& {360,720,1080,1440}
Interpretation of the Context
Let's interpret the context depending on the inputs and outputs.
For an input of 60 minutes there is one output of 360 calories.
For an input of 120 minutes there is one output of 720 calories.
For an input of 180 minutes there is one output of 1080 calories.
For an input of 240 minutes there is one output of 1440 calories.
Is the relation a function?
A function is a type of relation in which there is exactly one output for each input. Therefore, our relation is a function.
