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 shape. The function \(y = x^{3}\) is a cubic function. Let's check the key features: as \(x\) approaches positive infinity, \(y\) approaches positive infinity, and as \(x\) approaches negative infinity, \(y\) approaches negative infinity, which matches the given graph. The parabola \(y=x^{2}\) is a U - shaped curve (symmetric about the y - axis, opening upwards), the absolute value function \(y = |x|\) is a V - shaped curve, and the linear function \(y=mx + b\) is a straight line. The given graph has the characteristic shape of a cubic function \(y=x^{3}\).

Step2: Match with the given functions

We compare the graph with the four given functions:

• Line (\(y = mx + b\)): Straight line, does not match.
• Parabola (\(y=x^{2}\)): U - shaped, does not match.
• Cubic (\(y = x^{3}\)): Matches the shape (S - shaped, passing through the origin, with the end - behavior as described).
• Absolute Value (\(y=|x|\)): V - shaped, does not match.

Answer:

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