Question

1. the cost y (in dollars) of a cell phone plan is given by y = 30x, where x is the number of phones on the plan.

a) identify the independent and dependent variables.
b) you can have up to 4 phones on the plan. identify the domain and range.

Explanation:

Step1: Identify independent and dependent variables

The independent variable is the one that is changed or controlled in a scientific experiment. Here, \(x\) (the number of phones on the plan) is the independent variable. The dependent variable is the one that depends on the independent variable. Here, \(y\) (the cost of the cell phone plan) is the dependent variable.

Step2: Find the domain

The domain is the set of all possible values of the independent variable. Since you can have \(0\) to \(4\) phones on the plan, \(x\) can be \(0,1,2,3,4\). So the domain is \(\{0,1,2,3,4\}\)

Step3: Find the range

The range is the set of all possible values of the dependent variable. We use the equation \(y = 30x\).
When \(x=0\), \(y=30\times0 = 0\)
When \(x = 1\), \(y=30\times1=30\)
When \(x = 2\), \(y=30\times2 = 60\)
When \(x=3\), \(y=30\times3=90\)
When \(x = 4\), \(y=30\times4=120\)
So the range is \(\{0,30,60,90,120\}\)

Answer:

a) Independent variable: \(x\) (number of phones on the plan), Dependent variable: \(y\) (cost of the cell - phone plan)
b) Domain: \(\{0,1,2,3,4\}\), Range: \(\{0,30,60,90,120\}\)