Functions and graphs

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*.