Here is a graph showing the temperature in a town as a function of hours after 8:00 p.m.
The graph of a curve on the coordinate plane. The horizontal axis is labeled “time in hours after 8 pm” and the numbers 1 through 11 are indicated. The vertical axis is labeled “temperature in degrees Fahrenheit” and the numbers 45 through 60, in increments of 3 are indicated. The curve starts on the vertical axis at the point 0 comma 60, and moves downwards and to the right. It continues downward until reaching a minimum point of 8 comma 45, turns, and then moves upward and to the right, passing through the point 11 comma 57.
The graph of a function tells us what is happening in the context the function represents. In this example, the temperature starts out at 60∘ F at 8:00 p.m. It decreases during the night, reaching its lowest point about 8 hours after 8:00 p.m., or 4:00 a.m. Then it starts to increase again.
