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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?

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 class=

Answer :

indrawboy

Further explanation

Set A to set B is said to be a function if each member of set A pairs is exactly one member of set B

So, one value of x is only assigned to one value of y

If y is a function of x, then y = f (x)

Rate of Change function shows the comparison between 2 objects that change

If we use the notation function, the rate of Change from a function from a to b can be formulated as:

[tex] \large {\boxed {\boxed {\bold {ROC = \frac {f (a) -f (b)} {a-b}}}} [/tex]

ROC = rate of change

the domain and range of this roller coaster

The Domain is the X values, 0-360

written as (0,360)

The range is the Y values, 0-250

written as (0,250)

2. a. The slope of the initial climb

from points 0,0 and 70,250

slope = 250/70 = 3.57

b. equation from point 70,250

y-y1 = m (x-x1)

y-250 = 25/7 (x-70)

y = 25 / 7x-250 + 250

y = 25 / 7x

3. rate of change from (200, 200) to (300, 60) --- green hill

ROC = 60-200 / 300-200

ROC = -140/100

ROC = -1.4

4. rate of change from (200, 230) to (60, 30) - blue hill

ROC = 30-230 / 60-200

ROC = -200 / -140

ROC = 1.42

5. The greater the slope, the steeper the line

the blue hill is steeper than the green hill because the slope value of the blue hill is greater (steepness is not determined from the negative slope value)

6.the roller coaster is not a function, because there are 2 domain values ​​that are paired with the codomain for example points 200,200 and 200,230

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