# Identify the domain and range of `y=(-10)/x` and `y=1/(x+3)+3` I think the domain of the first graph is all real numbers except 0, and the range is all real numbers except 0. I think the domain of...

Identify the domain and range of `y=(-10)/x` and `y=1/(x+3)+3`

I think the domain of the first graph is all real numbers except 0, and the range is all real numbers except 0.

I think the domain of the second graph is all real numbers except -3 and the range is all real number except 3.

Is this right?

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your answer is correct, The domain must not be equal 0 because it makes the function meaningless., while the range is any real numbers except 0 in interval notation:

Domain:(-infinity,0) U(0, +infinity)

Range:(-infinity,0) U(0, +infinity)

In second given, , by equating the denominator to zero, we can get the restriction, x must not be equal to -3, so the domain is all set of real numbers except -3, while the range is all except 3.

Domain:(-infinity,-3) U(-3, +infinity)

Range:(-infinity,3) U(3, +infinity)