SOLUTION: what is the domain of the function y = 2 / x+6

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Question 107317: what is the domain of the function y = 2 / x+6
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a "function" must be single-valued+ which means "one and only one"; to each value of x+there is a unique value of y.
The values that x may assume are called the domain of the function, and those are the values for which the function is defined.
In the function +y+=+ax+%2B+b, the domain may include all+real+numbers+; consequently, x could be any+real+number.
But, there is one case in which the domain must be restricted, and that is the case when a denominator may+not+be+0.
So, in this function y+=+2+%2F%28+x%2B6%29 a denominator x%2B6 may not be equal to 0 because to divide by 0 doesn’t make a sense.
Let set it equal to 0 in order to find what x may not be in a domain:
x%2B6+=+0
x+=+0+%96+6
x+=+-6
Solution:
In a domain could be all other real numbers except -6.
Domain: (-+infinity, -6] and [-6,%2Binfinity)