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Describing Domain and Range

Describing Domain and Range 1.1 - Solution

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The domain of the function is the values rr can take. Here it's the number of subway rides. Since Clair only can pay for a whole number of rides, the domain is 0,1,2,30,1,2,3\ldots However, there is a highest value rr can take since she can't have a negative balance, b,b, on her card. Let's find the function's domain.
rr 172.75r17-2.75r bb
0{\color{#0000FF}{0}} 172.75017-2.75\cdot {\color{#0000FF}{0}} 1717
1{\color{#0000FF}{1}} 172.75117-2.75\cdot{\color{#0000FF}{1}} 14.2514.25
2{\color{#0000FF}{2}} 172.75217-2.75\cdot{\color{#0000FF}{2}} 11.511.5
3{\color{#0000FF}{3}} 172.75317-2.75\cdot{\color{#0000FF}{3}} 8.758.75
4{\color{#0000FF}{4}} 172.75417-2.75\cdot{\color{#0000FF}{4}} 66
5{\color{#0000FF}{5}} 172.75517-2.75\cdot{\color{#0000FF}{5}} 3.253.25
6{\color{#0000FF}{6}} 172.75617-2.75\cdot{\color{#0000FF}{6}} 0.50.5
7{\color{#0000FF}{7}} 172.75717-2.75\cdot{\color{#0000FF}{7}} -2.25\text{-} 2.25

Clair can only pay for 66 subway rides with the money she has on her OMNY card as 77 rides would make the balance on the card negative. D{0,1,2,3,4,5,6} D\text{: }\{0,1,2,3,4,5,6\}


In Part A we found all possible input and output values for the function.

(0,17)(1,14.25)(2,11.5)(0,17) \quad (1,14.25) \quad (2,11.5)
(3,8.75)(4,6)(5,3.25)(6,0.5)(3,8.75)\quad (4,6) \quad(5,3.25)\quad (6,0.5)

We graph the function by marking these points in a diagram.