Question

1. modeling real life a cell phone plan costs $30 for each line. (see example 4.)

a. does the situation represent a function? if so, identify the independent and dependent variables.
b. you can have a maximum of four lines on a plan. find the domain and range.

1. modeling real life a taxi company charges an initial fee of $2.80 plus $3.50 per mile traveled.

a. does the situation represent a function? if so, 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.

Explanation:

17.

Step1: Check if it's a function

For each number of lines, there is a unique cost. So it's a function.

Step2: Identify variables

The number of lines is the independent variable $x$, and the cost $y = 30x$ is the dependent variable.

Step3: Find domain

The number of lines $x$ can be $0,1,2,3,4$. So the domain is $\{0,1,2,3,4\}$.

Step4: Find range

When $x = 0,y=0$; when $x = 1,y = 30$; when $x = 2,y=60$; when $x = 3,y = 90$; when $x = 4,y=120$. So the range is $\{0,30,60,90,120\}$.

Step1: Check if it's a function

For each number of miles traveled, there is a unique cost. So it's a function.

Step2: Identify variables

The number of miles traveled $x$ is the independent variable, and the cost $y=2.80 + 3.50x$ is the dependent variable.

Step3: Find domain

The number of miles $x$ can range from $0$ to $20$ (inclusive). So the domain is $0\leq x\leq20$.

Step4: Find range

When $x = 0,y=2.80$; when $x = 20,y=2.80+3.50\times20=2.80 + 70=72.80$. So the range is $2.80\leq y\leq72.80$.

Answer:

a. Yes, it represents a function. Independent variable: number of lines; Dependent variable: cost.
b. Domain: $\{0,1,2,3,4\}$; Range: $\{0,30,60,90,120\}$

18.