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The domain of a function is the complete set of possible values of the independent variable in the function.

The domain of a function is the set of all possible x-values which will make the function “work” and will output real y-values.

When finding the domain, remember:

• The denominator (bottom) of a fraction cannot be zero
• The values under a square root and any even root sign must be positive

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually) of a function, after we have substituted the domain values.

The range of a function is the possible y values of a function that result when we substitute all the possible x-values into the function.

When finding the range, remember:

• Substitute different x-values into the expression for y to see what is happening. (Is y always positive? Always negative? Or maybe not equal to certain values?)
• Make sure you look for minimum and maximum values of y.