A plane that carries mail makes a round trip each day from Chicago to New York. It makes 2 intermediate stops on the way to New York and 1 intermediate stop on the way back to Chicago. Suppose you make a graph of the altitude of the plane for one day, with time on the horizontal axis and altitude on the vertical axis. How many times will the graph touch the horizontal axis?
Takeoff, each stop and landing. How many is that?
The graph will touch the horizontal axis every time the plane lands at one of the intermediate stops.
On the way to New York, the plane makes 2 intermediate stops. Therefore, the graph will touch the horizontal axis 2 times on this leg of the round trip.
On the way back to Chicago, the plane makes 1 intermediate stop. Therefore, the graph will touch the horizontal axis 1 time on this leg of the round trip.
In total, the graph will touch the horizontal axis 2 + 1 = 3 times.
To determine how many times the graph of the altitude of the plane will touch the horizontal axis, we need to consider the number of takeoffs and landings the plane makes throughout the day.
In a round trip from Chicago to New York, the plane makes 2 intermediate stops on the way to New York and 1 intermediate stop on the way back to Chicago. This means that the plane takes off from Chicago, lands at the first intermediate stop, takes off again, lands at the second intermediate stop, and finally lands at New York.
On the return trip, the plane takes off from New York, lands at the intermediate stop, takes off again, and lands at Chicago.
So, in total, the plane will touch the horizontal axis 5 times. These points represent the landings and takeoffs at each location throughout the day.