What is the domain and range of #y = x + 3 #?

1 Answer
Rafael
Feb 27, 2016

#domf=RR#
#ranf=RR#

Explanation:

#f(x)=x+3#

Domain

Is there any value of #x# that will make #f(x)# undefined?

The answer to this is no, so the domain is the set of all real numbers #RR#.

#domf=RR#

Range

You will notice that the graph of #x+3# is just a line, meaning it will intersect all values of #y# (since it increases and decreases without limit).

Therefore, the range is also the set of all real numbers #RR#.

#ranf=RR#

Just keep this in mind. When you're given a linear function, its domain and range are both the set of all real numbers (unless the problem tells you it isn't).

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