Question

11.) the function $y = 25x + 500$ represents your monthey rent $y$ (in dollars) when you pay $x$ days late.
a.) identify the independent and dependent variables.
b.) the domain is 0, 1, 2, 3, 4, and 5. what is the range?
12.) the function $y = 3.5x + 2.8$ represents the cost $y$ (in dollars) of a taxi ride of $x$ miles.
a.) identify the independent and dependent variables.
b.) you have enough money to travel at most 20 miles in the taxi. find the domain and range of the function.

Explanation:

11a.) Step1: Define independent variable

The independent variable is the input that is controlled, which is the number of days late, $x$.

11a.) Step2: Define dependent variable

The dependent variable depends on the input, which is the total rent cost, $y$.

11b.) Step1: Calculate $y$ for each domain value

For $x=0$: $y=25(0)+500=500$
For $x=1$: $y=25(1)+500=525$
For $x=2$: $y=25(2)+500=550$
For $x=3$: $y=25(3)+500=575$
For $x=4$: $y=25(4)+500=600$
For $x=5$: $y=25(5)+500=625$

11b.) Step2: Compile range values

Collect all calculated $y$ values.

12a.) Step1: Define independent variable

The independent variable is the input, which is the number of miles, $x$.

12a.) Step2: Define dependent variable

The dependent variable depends on the input, which is the taxi ride cost, $y$.

12b.) Step1: Identify valid domain values

The number of miles cannot be negative, and the maximum is 20, so domain is $0\leq x\leq20$ (all non-negative real numbers up to 20).

12b.) Step2: Calculate minimum range value

For $x=0$: $y=3.5(0)+2.8=2.8$

12b.) Step3: Calculate maximum range value

For $x=20$: $y=3.5(20)+2.8=72.8$

12b.) Step4: Compile range values

The range spans from the minimum to maximum $y$ value.

Answer:

11.) a.) Independent variable: $x$ (number of days late); Dependent variable: $y$ (total rent in dollars)
11.) b.) $\{500, 525, 550, 575, 600, 625\}$
12.) a.) Independent variable: $x$ (number of miles); Dependent variable: $y$ (taxi ride cost in dollars)
12.) b.) Domain: All real numbers where $0\leq x\leq20$; Range: All real numbers where $2.8\leq y\leq72.8$