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 has a cubic - like curve. The function \(y = x^{3}\) has a characteristic S - shaped curve (when considering the general cubic function, and for \(y=-x^{3}\) or other cubic transformations, the shape is still a cubic curve). The given graph's shape matches the general form of a cubic function.

Step2: Compare with given functions

• The line \(y = mx + b\) is a straight line, but the graph is curved, so it's not a line.
• The parabola \(y=x^{2}\) is a U - shaped curve (symmetric about the y - axis), the given graph is not U - shaped.
• The cubic function \(y = x^{3}\) (or its transformations) has a curve that changes direction twice, which matches the given graph.
• The absolute value function \(y = |x|\) has a V - shape, which is different from the given graph.

Answer:

The function of the graph is \(y = x^{3}\) (Cubic function)