Question

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1. it costs margaret between $20 and $25 to fill the gas tank of her car. she fills the tank once or twice a month. margaret maps the number of times she fills the tank to the total she spends on gas. what are the constraints on the domain and the range?

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Explanation:

Step1: Define domain variable

Let $n$ = number of tank fills per month. Margaret fills 1 or 2 times, so:
$n = 1$ or $n = 2$

Step2: Calculate minimum total cost

Minimum cost per fill is $\$20$. For $n=1$:
$\text{Cost}_{\text{min}} = 1 \times 20 = 20$
For $n=2$:
$\text{Cost}_{\text{min for 2 fills}} = 2 \times 20 = 40$

Step3: Calculate maximum total cost

Maximum cost per fill is $\$25$. For $n=1$:
$\text{Cost}_{\text{max}} = 1 \times 25 = 25$
For $n=2$:
$\text{Cost}_{\text{max for 2 fills}} = 2 \times 25 = 50$

Step4: Define domain and range

Domain is valid $n$ values. Range is all possible total costs.

Answer:

Domain: $\{1, 2\}$
Range: $\$20$ to $\$25$, $\$40$ to $\$50$ (or written as $[20,25] \cup [40,50]$ in interval notation)