Finding the domain is relatively easier - just check where the function makes no sense, and exclude them.

e.g. f(x) = 1/(1-x) has domain x =/= 1 (why? try plugging in x=1 into f(x)).

Finding the range is trickier. I usually sketch the function first and see what the output could be. So please do practice curve sketching.

Also very helpful is to know the domains and ranges of standard functions. For instance, log(x) has domain x>0 and range {all real numbers}; sin(x) has domain {all real numbers} and range [-1,1]; 1/x has domain x=/=0 and range {all real numbers except 0}, etc..

As a warning - plugging in the end points of the domain does not give you the range. e.g. with domain [-1,1] and f(x)=x^2, the range is [0,1], not {1} if you only check the end points. (why? sketch x^2 to find out!)

e.g. f(x) = 1/(1-x) has domain x =/= 1 (why? try plugging in x=1 into f(x)).

Finding the range is trickier. I usually sketch the function first and see what the output could be. So please do practice curve sketching.

Also very helpful is to know the domains and ranges of standard functions. For instance, log(x) has domain x>0 and range {all real numbers}; sin(x) has domain {all real numbers} and range [-1,1]; 1/x has domain x=/=0 and range {all real numbers except 0}, etc..

As a warning - plugging in the end points of the domain does not give you the range. e.g. with domain [-1,1] and f(x)=x^2, the range is [0,1], not {1} if you only check the end points. (why? sketch x^2 to find out!)

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