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

Answer 1

#x in RR, y in RR#

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#

Additionally, the graph illustrates this:

graph{x+3}

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Answer 2

Domain: All real numbers Range: All real numbers

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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