Question

At Zach's auto shop each mechanic can change the oil 3 cars per hour. Zach can have up to 4 mechanics working at a time. In a relationship between number of oil changes per hour and number of mechanics working identify the independent variable dependent variable domain and range

Answer 1

We know that:

Each mechanic can change the oil of 3 cars per hour.

The number of mechanics can change between 0 and a maximum of 4.

Then we can write the variable:

Y = number of oil changes per hour.

Y = 3*X

Where X is the number of mechanics working.

The independent variable is X (number of mechanics), because is the one that Zach can change, and the dependent is Y (number of oil changes) because this depends on the value of X.

Now, the domain will be: {0, 1, 2, 3, 4}

The possible numbers of mechanics working at the same time.

And for the range we must replace those values in our equation, and see the possible values of Y.

Y(0) = 3*0 = 0

Y(1) = 3*1 = 3

Y(2) = 3*2 = 6

Y(3) = 3*3 = 9

Y(4) = 3*4 = 12

Then the range is: {0, 3, 6, 9, 12}