If y is a positive integer, for how many different values of y is sqrt ^ 3 144 / y a whole number?

second option.

Step-by-step explanation:

We need the remember that:

Therefore, the radicand (In this case ) must be a perfect cube in order to get a whole number.

Remember that a perfect cube are the numbers that have exact cube roots. Therefore, "y" must be a factor of 144.

Now, we need to descompose 144 into its prime factors:

Then, the factors of 144 are:

Substitute values into to check:

 (Perfect cube: )

(Perfect cube: )

Therefore, for 2 different values of "y"  ( and ) is a whole number.

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)