• multiple functions can be added, subtracted, multiplied, and divided to create new functions
• functions are typically named f(x), g(x), and h(x), but any letter can be used
• these names do not mean anything, they are just to differentiate multiple functions

Combining Functions Algebraically

• plug in the equation for each function, then simplify (factor if nessecary)

Domain of a Combined Function

• the domain of a combined function is the area both functions have in common
• in h(x) = f(x)/g(x), g(x) cannot equal 0, so for any values of x that make g(x) equal 0, that is also not in the domain of h(x)

Range of a Combined Function

• graph the combined function using a graphing calculator
• if the graph continues indefinitely up and down, the range is all real numbers
• if there is a maximum (y less than or equal to a number) or a minimum (y greater than or equal to a number), use the graphing calculator functions to find the minimum point or maximum point