non-linear graphs\ngraphs\nline: y = mx + b\nparabola: y = x²\ncubic : y = x³\nabsolute value y = |x|
non-linear graphs\ngraphs\nline: y = mx + b\nparabola: y = x²\ncubic : y = x³\nabsolute value y = |x|
Answer
Explanation:
Step1: Analyze the graph's shape
The graph passes through the origin, is symmetric about the origin (odd function), and has a curve that rises steeply for positive (x) and falls steeply for negative (x), matching the cubic function's behavior.
Step2: Compare with given functions
- Line ((y = mx + b)): Linear, straight line. The graph is curved, so not a line.
- Parabola ((y = x^2)): Symmetric about the (y)-axis (even function), U - shaped. The graph is symmetric about the origin, so not a parabola.
- Cubic ((y = x^3)): Has the shape of a curve that passes through the origin, is symmetric about the origin, and has the characteristic "S - like" curve for (y=x^3).
- Absolute Value ((y = |x|)): V - shaped, symmetric about the (y)-axis. The graph does not have a V - shape, so not absolute value.