SOLUTION: Find the domain: s(y) = 3y/(y+5) Thanks!

Question 120452This question is from textbook Trigonometry
: Find the domain:
s(y) = 3y/(y+5)
Thanks! This question is from textbook Trigonometry

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given function

Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of y that make the denominator zero, then we must exclude them from the domain.

Subtract 5 from both sides

Combine like terms on the right side

Since makes the denominator equal to zero, this means we must exclude from our domain

So our domain is:

which in plain English reads: y is the set of all real numbers except

So our domain looks like this in interval notation

note: remember, the parenthesis excludes -5 from the domain

If we wanted to graph the domain on a number line, we would get:

Graph of the domain in blue and the excluded value represented by open circle

Notice we have a continuous line until we get to the hole at (which is represented by the open circle).
This graphically represents our domain in which y can be any number except y cannot equal -5

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