Here are graphs of two functions, each representing the cost of riding in a taxi from two companies—Friendly Rides and Great Cabs.

For each taxi, the cost of a ride is a function of the distance traveled. The input is distance in miles, and the output is cost in dollars.

2 graphs. Horizontal axis, 0 to 7, distance, miles. Vertical axis, 0 to 16 by 4’s, cost, dollars. Dotted graph starts flat, then increases. Passes through 2 comma 4 point 2 5. Solid graph starts flat then increases. Passes through 2 comma 5 point 7. They intersect near 4 point 5 comma 10.

• The point $(2,5.70)$ on one graph tells us the cost of riding a Friendly Rides taxi for 2 miles.
• The point $(2, 4.25)$ on the other graph tells us the cost of riding a Great Cabs taxi for 2 miles.

We can convey the same information much more efficiently by naming each function and using function notation to specify the input and the output.

• Let’s name the function for Friendly Rides function $f$.
• Let's name the function for Great Cabs function $g$.
• To refer to the cost of riding each taxi for 2 miles, we can write $f(2)$ and $g(2)$.
• To say that a 2-mile trip with Friendly Rides will cost $5.70, we can write $f(2)=5.70$.
• To say that a 2-mile trip with Great Cabs will cost $4.25, we can write $g(2)=4.25$.

In general, function notation has this form:

It is read “$f$ of $x$” and can be interpreted to mean that $f(x)$ is the output of a function $f$ when $x$ is the input.

The function notation is a concise way to refer to a function and describe its input and output, which can be very useful. Throughout this unit and the course, we will use function notation to talk about functions.