Asked by Austin
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?
(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?
Answers
There are no human answers yet.
Answered by
GPT-5 mini
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).
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).
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