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Describing Domain and Range

Describing Domain and Range 1.10 - Solution

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The minimum number of traveled miles is 0.0. To determine the cost that corresponds with this distance, we can substitute x=0x=0 into the equation and solve for y.y.
y=4x+2.5y=4x+2.5
y=4(0)+2.5y=4( {\color{#0000FF}{0}})+2.5
y=2.5y=2.5
The minimum cost of a taxi ride is $2.50.\$2.50. It is given that there is enough money to travel most 3030 miles. We can consider this the maximum distance. To determine the cost of such a ride, we will substitute x=30x=30 into the equation and solve for y.y.
y=4x+2.5y=4x+2.5
y=4(30)+2.5y=4({\color{#0000FF}{30}})+2.5
y=120+2.5y=120+2.5
y=122.5y=122.5
Since y=122.5y=122.5 when x=30,x=30, the maximum cost of a ride is $122.50.\$122.50. From our work above, we have established that Kareem can travel from 00 to 3030 miles and the cost is from $2.50\$2.50 to $122.50.\$122.50. These values represent the lower and upper boundaries of our domain and range. D0x30R2.5y122.5\begin{aligned} D\text{: }& 0\leq x \leq 30\\ R\text{: }& 2.5\leq y \leq 122.5 \end{aligned}