a Identify the initial cost and then adjust it to consider the cost of each ride.
B
b Start by creating a table. Based on the table, create the other required representations.
C
c Review the definitions of domain and range, then use your work from Part B to find them.
A
a A =30 + 2r
B
b See solution.
C
cDomain: {0, 1, 2, 3, 4, 5 }
Range: {30, 32, 34, 36, 38, 40 } Is it a Function? Yes.
Practice makes perfect
a Let's write an equation for the amount of money a person spends at the amusement park. The admission and food is a $30 flat fee. This will be a constant in our equation. Each ride costs an additional $2. With this, the total amount spent A will be $30 plus $2 per ride r.
A =30 + 2r
b We will now represent the relation from Part A using a table, graph, and mapping diagram. Let's begin with the table. For this, we need to consider the possible inputs and find the corresponding outputs by substituting values in the relation. We are told that each rider will ride between 0 and 5 rides, so those are our inputs.
Rides r
A=30+2r
Amount A
0
A = 30 + 2( 0)
30
1
A = 30 + 2( 1)
32
2
A = 30 + 2( 2)
34
3
A = 30 + 2( 3)
36
4
A = 30 + 2( 4)
38
5
A = 30 + 2( 5)
40
Now, we can obtain the graph of the relation by plotting the points from the table.
Finally, to create the mapping diagram, we can look at the table once more. We have to order all the inputs and outputs and match them accordingly.
c To find the domain and range, recall that in a relation we have ordered pairs ( x,y). The x-values are the inputs and the y-values are the outputs. The domain is all possible inputs for a relation, while the range is all possible outputs. By looking at the representations in Part B, we can see the ordered pairs and list these values to have the domain and range.
Domain:& {0, 1, 2, 3, 4, 5 }
Range:& {30, 32, 34, 36, 38, 40 }
Furthermore, we can see that this relation is a function because each value in the domain is paired with exactly one value in the range. This can be seen most clearly in the mapping diagram.
