Design a roller coaster portfolio
algebra 2 a: functions, equations, and graphs (modified)

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 analyze a roller coaster design which i have made. i have drawn the x and y axes and plotted points for you. using the attached picture, answer the following questions:

1. what is the domain and range of this roller coaster?
domain: 60,70,130,200,200,300 range: 30,250,130,200,230,60

2. look at the initial climb. (it is highlighted in pink) , the coordinates at its peak are (70, 250).
a. find the slope. show your work.

slope = 1.125

b. write the equation of the line that represents the initial climb in y=mx + b form.

y=

3. look at the second hill. (it is highlighted in green.) what is the rate of change from the top of the hill (200, 200) to the bottom (300, 60)? show how you got your answer.

4. look at the third hill. (it is highlighted in light blue.) what is the rate of change from the top of that hill (200, 230) to its bottom (60, 30)? show how you got your answer.

5. which hill is steeper—the green or the blue? how do you know that hill is steeper?

6. is the roller coaster a function? why or why not?