Designing a roller coaster involves combining engineering principles, physics, and creativity to create a thrilling and safe ride experience.
Label the x- and y-axes.
The x-axis represents the horizontal distance from the roller coaster cart to the starting point, and the y-axis represents the height of the roller coaster cart.
Plot ordered pairs on the initial climb and determine the slope.
The slope of the initial climb is positive, which means that the roller coaster is gaining speed.
What is the equation of the line that represents your initial climb?
The equation of the line that represents the initial climb is y = mx + b, where m is the slope and b is the y-intercept.
To determine the equation of the line, we need to know two points on the line.
We can use the points (0, 0) and (10, 100) to determine the equation of the line.
m = (100 - 0) / (10 - 0)
m = 10
b = 0
The equation of the line that represents the initial climb is y = 10x.
What is the domain and range of your roller coaster?
The domain of a function is the set of all possible input values. The range of a function is the set of all possible output values.
The domain of the roller coaster function is all non-negative numbers.
This means that the roller coaster can start at any height above the ground, but it cannot start below the ground.
The range of the roller coaster function is all real numbers. This means that the roller coaster can reach any height above the ground.
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?
The rate of change of a function is the slope of the line that represents the function. A steeper slope indicates a faster rate of change.
Is your roller coaster a function? Why or why not?
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.