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 (exponent 2), not a line.

2) Example table values (s, A = s^2):
- s = 0 → A = 0
- s = 1 → A = 1
- s = 2 → A = 4
- s = 3 → A = 9
- s = 4 → A = 16
(you can also use fractions, e.g. s = 0.5 → A = 0.25)

3) If you restrict s to allowable side lengths (s ≥ 0) the graph is increasing — A gets larger as s increases. (On all real s the parabola decreases for s < 0 and increases for s > 0, with a minimum at s = 0.)

4) Domain: all nonnegative real numbers, s ≥ 0 (i.e. [0, ∞)), since side length cannot be negative.