Question

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

Explanation:

Step1: Identify the graph shape

The given graph has a V - shape with the vertex at the origin (0,0). The left side has a negative slope and the right side has a positive slope.

Step2: Match with the given functions

• The line \(y = mx + b\) is a straight line (linear), but our graph is non - linear (V - shaped), so it's not a line.
• The parabola \(y=x^{2}\) is a U - shaped curve, not a V - shape, so it's not a parabola.
• The cubic function \(y = x^{3}\) has a different shape (it passes through the origin and has a point of inflection, not a V - shape), so it's not a cubic.
• The absolute value function \(y=\vert x\vert\) has a V - shape with the vertex at (0,0), and for \(x\geq0\), \(y = x\) (positive slope) and for \(x<0\), \(y=-x\) (negative slope), which matches the given graph.

Answer:

The graph represents the absolute value function \(y = \vert x\vert\)