How do you find the domain and range of #y = x + 3#?

1 Answer

Answer:

#x in RR, y in RR#

Explanation:

The Domain is the list of all allowable #x# values. Sometimes, equations have #x# values that can't be used. Here are a couple of examples:

#1/x# - since we can't divide by 0, #x!=0#

#sqrtx# - since we can't get real number solutions to a negative number under the square root sign, we tend to say that we can't have negative values, and so #x>=0#

In our case, there are no values of #x# that are disallowed. And so any real value can be an #x# value, or

#x in RR# - which says #x# can be any real value

The Range is the list of all values arising from the domain (which in this case are the #y# values).

In our case, when #x# is large, so will #y#. When #x# is a large negative, so will #y#. In fact, we can arrive at any value #y# by picking the correct value of #x#. And so we can say:

#y in RR#

And we can see this in the graph:

graph{x+3}