Introduction to Functions

Consider a car entering a parking garage that charges for the time spent inside.

This situation can be described using a function—a rule that gives a specific cost for each hour of parking.

The domain of the function—the set of all valid inputs—is non-negative hours, a physical constraint since time can't be negative.

As each hour passes, the total cost increases by the same amount, forming a predictable, steady pattern.

This function can be represented in four ways: verbal, algebraic, visual, and numerical, each showing how inputs connect to outputs.

The verbal form says the cost is four dollars to enter plus three dollars per hour.

This relationship is written as a formula where the base fee is combined with a charge that increases by three for each hour.

The visual form is a plot that begins at four and rises steadily with time.

The numerical form is a table that matches domain values—non-negative hours—to range values, which are total costs.

Another example of a function is the elevation change of a hiking trail, with distance as input and elevation as output. This forms a smooth, continuous curve.