Homefun 2-11+
How Big Will It Go?
Stretch
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Consider the pattern above for the next three questions with the following facts:
• The perimeter of the square in Figure 1 is 4.
• The area of the square in Figure 1 is 1.
• Each new square added has side length 1/3 of the previous square.
[1] Create a sequence of numbers for the following:
a. Number of new squares in Figure 𝑛.
b. Perimeter of all new squares in Figure 𝑛.
c. Area of new squares in Figure 𝑛.
[2] What is the total perimeter of all squares in Figure 𝑛? The total area of all squares in Figure 𝑛?
[3] If this process shown in the figures could repeat forever, what conclusions can you make about
the perimeter and area of all squares in the figures?
Review
[4] Find the domain and range of each function.
a. 𝑓(𝑥) = 3𝑥 + 2
b. 𝑔(𝑥) = 2 ∙ 3!