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# Describing Domain and Range

## Describing Domain and Range 1.1 - Solution

a
The domain of the function is the values $r$ can take. Here it's the number of subway rides. Since Clair only can pay for a whole number of rides, the domain is $0,1,2,3\ldots$ However, there is a highest value $r$ can take since she can't have a negative balance, $b,$ on her card. Let's find the function's domain.
$r$ $17-2.75r$ $b$
${\color{#0000FF}{0}}$ $17-2.75\cdot {\color{#0000FF}{0}}$ $17$
${\color{#0000FF}{1}}$ $17-2.75\cdot{\color{#0000FF}{1}}$ $14.25$
${\color{#0000FF}{2}}$ $17-2.75\cdot{\color{#0000FF}{2}}$ $11.5$
${\color{#0000FF}{3}}$ $17-2.75\cdot{\color{#0000FF}{3}}$ $8.75$
${\color{#0000FF}{4}}$ $17-2.75\cdot{\color{#0000FF}{4}}$ $6$
${\color{#0000FF}{5}}$ $17-2.75\cdot{\color{#0000FF}{5}}$ $3.25$
${\color{#0000FF}{6}}$ $17-2.75\cdot{\color{#0000FF}{6}}$ $0.5$
${\color{#0000FF}{7}}$ $17-2.75\cdot{\color{#0000FF}{7}}$ $\text{-} 2.25$

Clair can only pay for $6$ subway rides with the money she has on her OMNY card as $7$ rides would make the balance on the card negative. $D\text{: }\{0,1,2,3,4,5,6\}$

b

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

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

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