Remember Clare on the Ferris wheel? In the table, we have the function which gives her height above the ground, in feet, seconds after starting her descent from the top. Today Clare tried out two new Ferris wheels.

• The first wheel is twice the height of  and rotates at the same speed. The function gives Clare's height , in feet, seconds after starting her descent from the top.
• The second wheel is the same height as  but rotates at half the speed. The function gives Clare's height , in feet, seconds after starting her descent from the top.

1. Complete the table for the function .

   0	212
   20	181
   40	106
   60	31
   80	0

2. Explain why there is not enough information to find the exact values for  and .
3. Complete as much of the table as you can for the function , modeling Claire's height on the second Ferris wheel.
4. Express and in terms of . Be prepared to explain your reasoning.

Function is a transformation of function due to a scale factor.

Functions k and P on coordinate grid. Horizontal x axis from negative 6 to 6 by 2’s. Vertical y axis from negative 6 to 6 by 2’s. Each function has three connected segments. Function P, solid line starts at negative 3 comma negative 1, goes to negative 1 comma negative 2, then 1 comma 2, and ends at 4 comma 0. Function K, dotted line, starts at negative 3 comma negative 3, goes to negative 1 comma negative 6, then 1 comma 6, and ends at 4 comma 0.

1. Write an equation for in terms of .
2. On the same axes, graph the function where .
3. The highest point on the graph of is . What is the highest point on the graph of a function where ? Explain or show your reasoning.
4. The point furthest to the right on the graph of is . If the point furthest to the right on the graph of a function is , write a possible equation for in terms of .

A sphere, cylinder, and cone all have the same radius, . The cone and cylinder each have a height of 5 units.

1. Write an equation for the volume of each solid as a function of the radius.
2. Write an equation to describe the new volume of each solid if the radius doubles. How much larger is the volume of each new solid?
3. If the original radius is 3 units, what is the volume of each new solid after the radius doubles?