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Question 95507: I NEED MORE SPECIFICS ON HOW TO FIND THE DOMAIN AND RANGE OF THE FOLLOWING FUNCTION:
f(x)=2x-1
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Domain and Range on your problem are both "all Real Numbers" because there
is nothing in the rule of the function that restricts x or y.
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What does restriction look like?
Example: y = 3/(x-2) ; x cannot be 2; domain is : all Real except x=2
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Example: y = sqrt(x+3): x+3 must be >=0; x must be >=-3 and that is the domain.
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Example: y = log (x-2): x-2 must be >=0; x must be >=2 and that is the domain
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So, check the denominators; check even-root expressions; check log expressions
when looking for restrictions in the domain. If none of these is present the
domain is "all Real number".
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The Range is something else:
Example: y= x^2 + 4
Since x^2 is always >= 0 , x^2+4 is always >=4 so the Range is >=4.
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Hope these examples help.
General Rule: Assume the domain is unrestricted unless you can see a reason
to restrict it.
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Cheers,
Stan H.
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