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 characteristic "S - curve" shape, passing through the origin, with one end going down as \( x \) decreases and up as \( x \) increases.

Step2: Compare with given functions

• The line \( y = mx + b \) is linear (straight line), but the graph is curved, so not a line.
• The parabola \( y=x^{2}\) is a U - shaped curve (symmetric about the y - axis), but the given graph is not symmetric about the y - axis in the same way (it has a different curvature and direction for negative and positive \( x \) values).
• The cubic function \( y = x^{3}\) has a graph that passes through the origin, is symmetric about the origin (odd function), and has the "S - curve" shape as seen in the graph.
• The absolute value function \( y=\vert x\vert\) is a V - shaped graph, which does not match the given curve.

Answer:

The graph represents the cubic function \( y = x^{3}\)