Question

The equation for the area of a square could be written: A=s2
(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?

Answer 1

1) Nonlinear. A = s^2 is a quadratic function (not a line).

2) Example values (s, A = s^2):
- (0, 0)
- (1, 1)
- (2, 4)
- (3, 9)
- (4, 16)
- (0.5, 0.25)
(If you allow negative s mathematically: (−1, 1), (−2, 4), …)

3) For physically meaningful side lengths (s ≥ 0) the graph is increasing: as s gets larger, A increases. (As a parabola overall, A = s^2 decreases for s < 0 and increases for s > 0, with a minimum at s = 0.)

4) Domain: all nonnegative real numbers (s ≥ 0) in the context of side lengths. Mathematically, the function is defined for all real numbers (s ∈ ℝ).