Introduction: Have you ever ridden or seen a roller coaster in action? Did you know that the algebra that you have learned in this unit is related to the math that engineers use to design roller coasters? Engineers want roller coasters to be fun and scary, but also safe. Directions: For this portfolio, you will use your knowledge of functions to design a roller coaster. You will draw a short roller coaster on graph paper, plot ordered pairs on its path, and determine the slope, or rate of change, along the ride. Roller Coaster Design Instructions Submit responses to the following items, and be sure to show all of your work. 1. 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. o In order to gain speed, the roller coaster should have an initial climb, at least two hills, and one loop. 2. 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. 3. Plot ordered pairs on the initial climb and determine the slope. 4. What is the equation of the line that represents your initial climb? 5. What is the domain and range of your roller coaster? 6. 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? 7. Is your roller coaster a function? Why or why not?

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