# Roller Coaster Assignment

### By: Sukhpreet Kaur

## Summary

I created my roller coaster by manipulating the parent equation of each function. For example: y= x² is the parent function for a quadratic. I knew that I needed to apply transformations to this particular function. So, to transform this function I had to change the “a” , “k”, “d” and “c” value of the quadratic to fit in the form of: a(kx-d)²+c. I essentially used vertical stretches / compressions horizontal stretches / compressions, vertical shifts: up or down and horizontal shifts to the left or right. I also applied reflections in the x and y axis to reflect certain functions in some parts of my roller coaster. Furthermore, it was important to apply certain restrictions to my functions and to essentially ignore the second, third and fourth quadrants (as they would make the roller coaster go underground and go backwards with negative height and time). One of the major difficulties I experienced when making my roller coaster was staying within the 100 second time limit. To overcome this difficulty, I had to alter the restrictions on my functions or change there domains to complete the ride in 100 seconds. Furthermore at the beginning, a difficulty I encountered was connecting the functions together to form the roller coaster. I had to use guess and check (or trial and error) to find the correct "a", "k" , "d" and "c" values. I also realized that I had to restrict the domain of my functions at certain times to create it.

## Written Report: Description of Functions of Height vs Time

## Equations of the Functions:

**Polynomial Function**

y= 2(x-5)³+100

{2≤x≤8.419}

**Sinusoidal Function**

y= -5cos(x)+170

{8.307≤x≤5.18pi}

**Quadratic Function**

y= -(x-27.5)²+300

{16.287≤x≤33}

**Rational Function**

y= 2x²/2x-58

{33≤x≤71}

**Exponential Function**

y= -3^(x-80.3)+120

{71≤x≤82}

**Logarithmic Function**

y= -log(x-82)+100

{82≤x≤87.06}

**Linear Function**

y= -6.9x+700

{87.06≤x≤100}

**Linear Function**

y=20x+10

{0≤x≤2.3}