Key Concepts

• Division by [latex]0[/latex] is undefined.
• Values of the input variable that would make the denominator of a rational expression equal to zero must be stated and excluded from the domain of a function containing the expression.
• To restrict the domain of a rational function, set the denominators each equal to zero. Solve for the variable in each denominator and exclude those solution sets.
• Taking an even root (e.g., a square root) of a negative number yields an unreal result.
  • Values of the input variable that would place a negative amount under an even root must be stated and excluded from the domain of a function containing the expression.
• To restrict the domain of a function containing one radical, set the radicand greater than or equal to zero. Solve for the variable. The resulting solution set is the domain of the function.
• The domain of a function is read from the x-axis (the horizontal, or independent, axis) of the graph of the function.
• The range of a function is read from the y-axis (the vertical, or dependent axis) of the graph of the function.

Glossary

domain

the set of all possible input into a function

radical function 

a function containing a radical

radicand 

the value underneath the radical sign

range

the set of all possible output from a function

rational function 

a function containing a rational expression (a fraction)