Question

The equation for the area of a square could be written: A=s2
𝐴
=
𝑠
2
(4 points)
1) Is this a linear or nonlinear function?

2) What are some of the values in the table where s is the side length and A is the area?

3) When you plot these points, is the graph increasing or decreasing?

4) What numbers would be included in the domain?


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Answer 1

1) Nonlinear — it’s a quadratic function (A = s^2).

2) Sample values (s, A):
- s = 0 → A = 0
- s = 1 → A = 1
- s = 2 → A = 4
- s = 3 → A = 9
- s = 4 → A = 16
(you can also have s = 0.5 → A = 0.25, etc.)

3) For side lengths (s ≥ 0) the graph is increasing: as s gets larger, A = s^2 increases (and increases faster as s grows). Mathematically, s^2 decreases on (−∞,0] and increases on [0,∞), but negative s are not meaningful for side length.

4) Domain (in this context of side lengths): all nonnegative real numbers, s ≥ 0 (i.e., [0, ∞)).