The domain of a function is the complete set of possible values of the independent variable. The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
When finding the domain, remember:
The denominator (bottom) of a fraction cannot be zero
The number under a square root sign must be positive in this section
The range is the resulting y-values we get after substituting all the possible x-values.
Revenue: R ( x ) / x = 30 - 0.25 x R ( x ) = 30 x - 0.25 x² Profit: P ( x ) = 30 x - 0.25 x² - 200 P ` ( x ) = 30 - 0.5 x 30 - 0.5 x = 0 0.5 x = 30 x = 60 P max = 30 · 60 - 0.25 · 3600 - 200 = $700 Answer: I should sell 60 tickets to maximize the profit.