Analyzing Functions in Context

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	$120$
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. $\begin{aligned} D\text{: }&\{0,1,2,3,4\} \\ R\text{: }&\{120,128,136,144,152 \} \end{aligned}$

Analyzing Functions in Context 1.11 - Solution