Unit 1, Lesson 9
What’s the Equation?
Algebra 2
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On the grid, draw a square of side length 1 in the lower left corner. Draw another square of side length 1 that shares a side directly above the first square. Next, add a 2-by-2 square, with one side along the sides of both of the first two squares. Next, add a square with one side that goes along the sides of the previous two squares you created. Then do it again.
Pause here for your teacher to check your work.
The model we use for a function can depend on what we want to do.
For example, an 8-by-10 piece of paper has area 80 square inches. Picture a set of pieces of paper, each half the length and half the width of the previous piece.
A set of 4 pieces of paper, landscape. The first is the largest paper. The second, is half the length and half the width of the first. The third and fourth, are each half the length and half the width of the previous piece of paper.
Define the sequence
But for
If we wanted to define the
Graph of a discrete function, A, origin “O”. Horizontal axis, “piece number”, with scale 0 to 6, by 1’s. Vertical axis, “area in square inches”, with scale 0 to 100, by 20’s. Coordinates plotted 1 comma 80, 2 comma 20, 3 comma 5, 4 comma1 point 2 5, 5 comma 0 point 3 1 2 5 , and 6 comma 0 point 0 7 8 1 2 5 .
We can use this definition to calculate a value of