Question

non-linear graphs
graphs
line: y = mx + b
parabola: y = x²
cubic : y = x³
absolute value y = |x|

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.

Answer:

Cubic (or \(y = x^3\))