- Draw the side view of your roller coaster on graph paper. For the sake of simplicity, assume that your roller coaster track never turns left or right. In order to gain speed, the roller coaster should have an initial climb, at least two hills, and one loop.
- Label the x- and y-axes. The value of x measures the horizontal distance from the roller coaster cart to the starting point, and the value of y represents the height of the roller coaster cart.
- Plot ordered pairs on the initial climb and determine the slope.
- What is the equation of the line that represents your initial climb?
- What is the domain and range of your roller coaster?

Plot ordered pairs at the top and the end of each hill. Find the rate of change to determine which hill is steeper? How do you know that hill is steeper?

– Is your roller coaster a function? Why or why not?