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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 | $120$ |

Price per ticket | $8$ |

Increase in income after selling $t$ tickets | $8x$ |

Income after selling $t$ tickets | $f(x)=8x+120$ |

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

b

We are told that Patricia has $4$ tickets left. Therefore, a reasonable domain would be integers from $0$ to $4.$ Let's determine the range using a table of values.

Number of Tickets | Calculation | Income |
---|---|---|

${\color{#0000FF}{0}}$ | $8\cdot{\color{#0000FF}{0}}+120$ | $\$120$ |

${\color{#0000FF}{1}}$ | $8\cdot{\color{#0000FF}{1}}+120$ | $\$128$ |

${\color{#0000FF}{2}}$ | $8\cdot{\color{#0000FF}{2}}+120$ | $\$136$ |

${\color{#0000FF}{3}}$ | $8\cdot{\color{#0000FF}{3}}+120$ | $\$144$ |

${\color{#0000FF}{3}}$ | $8\cdot{\color{#0000FF}{4}}+120$ | $\$152$ |

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