Can someone help find the domain of the rational function below?

Question

anonymous · Answer

$$f(y) = \frac{ y + 6 }{ y^2 - 6y }$$

mathstudent55 · Answer

What can a denominator NOT be equal to?

anonymous · Answer

0 or 1?

mathstudent55 · Answer

0. A denominator can be one bec division by one is permitted. Since division by zero is undefined, a denominator cannot be zero.

mathstudent55 · Answer

To find the domain of the function, set the denominator equal to zero and solve for y. Whichever values you get for y are the values the domain cannot have.

mathstudent55 · Answer

In other words, solve this equation for y:
y^2 - 6y = 0

anonymous · Answer

I know it would be something like (y + )(y - )
but I always get lost to what numbers to put in. Would it 3 & 2?

mathstudent55 · Answer

Actually it's easier that that bec it's only two terms.
Factor the largest factor you can out of y^2 and -6y

anonymous · Answer

so It would be y(y - 6)

y = 0
and 

y - 6 = 0
y = 6

anonymous · Answer

What would be the domain though? Its asking to write the answer in interval notation.

mathstudent55 · Answer

Exaclty. Excellent work.

mathstudent55 · Answer

Since y = 0 and y = 6 would make the denominator zero, the domain is all real numbers except y = 0 and y = 6.

mathstudent55 · Answer

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