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 given graph has a cubic - like curve. Let's recall the properties of the cubic function \(y = x^{3}\). The function \(y=x^{3}\) has a point of inflection at the origin \((0,0)\) and as \(x\) increases, \(y\) increases, and as \(x\) decreases (for negative \(x\)), \(y\) decreases (since for \(x=-a,a > 0\), \(y=-a^{3}\) which is negative and as \(x\) becomes more negative, \(y\) becomes more negative, and for positive \(x\), \(y\) is positive and increases as \(x\) increases). But wait, the given graph here: when \(x\) is negative (left of the y - axis), the graph is in the positive \(y\) - region and as \(x\) increases towards 0, \(y\) decreases, and when \(x\) is positive (right of the y - axis), \(y\) is negative and decreases as \(x\) increases. Let's consider the function \(y=-x^{3}\) (a reflection of \(y = x^{3}\) over the \(x\) - axis). For \(y=-x^{3}\), when \(x=-a,a>0\), \(y=-(-a)^{3}=a^{3}>0\), when \(x = 0\), \(y = 0\), and when \(x=a,a > 0\), \(y=-a^{3}<0\). The shape of the graph in the picture matches the shape of the cubic function \(y=-x^{3}\) (which is a type of cubic graph, since cubic functions have the general form \(y = ax^{3}+bx^{2}+cx + d\), and \(y=-x^{3}\) is a cubic function with \(a=- 1,b = c=d = 0\)). The other functions: the line \(y=mx + b\) is linear (straight line), the parabola \(y = x^{2}\) is a U - shaped curve opening upwards, and the absolute value function \(y=\vert x\vert\) is a V - shaped curve with the vertex at the origin opening upwards. So the graph in the picture is a cubic graph.

Answer:

Cubic (specifically a transformed cubic function, but the type of non - linear graph here is Cubic)