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Analyzing Functions in Context

Analyzing Functions in Context 1.11 - Solution

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a

To write a function for this situation, we will express each piece of given information algebraically. From there we combine the parts to form the function.

Verbal Expression Algebraic Expression
Value of tickets already sold 120120
Price per ticket 88
Increase in income after selling tt tickets 8x8x
Income after selling tt tickets f(x)=8x+120f(x)=8x+120

Thus, a function describing the situation can be written as f(x)=8x+120.f(x)=8x+120.

b

We are told that Patricia has 44 tickets left. Therefore, a reasonable domain would be integers from 00 to 4.4. Let's determine the range using a table of values.

Number of Tickets Calculation Income
0{\color{#0000FF}{0}} 80+1208\cdot{\color{#0000FF}{0}}+120 $120\$120
1{\color{#0000FF}{1}} 81+1208\cdot{\color{#0000FF}{1}}+120 $128\$128
2{\color{#0000FF}{2}} 82+1208\cdot{\color{#0000FF}{2}}+120 $136\$136
3{\color{#0000FF}{3}} 83+1208\cdot{\color{#0000FF}{3}}+120 $144\$144
3{\color{#0000FF}{3}} 84+1208\cdot{\color{#0000FF}{4}}+120 $152\$152

Thus, we can write the domain and range as the following. D{0,1,2,3,4}R{120,128,136,144,152}\begin{aligned} D\text{: }&\{0,1,2,3,4\} \\ R\text{: }&\{120,128,136,144,152 \} \end{aligned}