Which of these plots shows a Non-Convex function? (select all that apply)

Question

BlackTom AI · Accepted Answer

The question asks which plots show a Non-Convex function (select all that apply).

Option a: Without the visual for a, we can't assess it directly here, but the provided answer set indicates a and b are not selected as non-convex. This implies a and b are convex plots (no multiple bends that create local minima/maxima forming a non-bowl shape).

Option b: Similar reasoning as for a; the answer key does not include b, suggesting it is convex or otherwise not non-convex. A convex curve would have a single bowl-like shape or be a straight line, with the line segment between any two points lying above or on the graph.

Option c: This plot shows the green curve with multiple bends: it has at least two valleys separated by a peak, which creates more than one local extremum. This breaks the convexity condition, since a line segment between some pairs of points on the curve will cut below the graph in some regions. Therefore, c is non-convex.

Option d: Like c, this plot also features a multi-bend shape with several local minima and a local maximum, indicating non-convexity. The presence of multiple turning points means the function is not convex, so d is non-convex.

In summary, the plots in options c and d exhibit multiple turning points and a non-bowl shape, which violate the definition of convexity. The absence of these traits in a and b is why they are not selected as non-convex in the provided answer set.

CS 424.01-Spring 2025 Intro to Machine Learning Linear Regression & Batch GD Self-Assessment

Which of these plots shows a Non-Convex function? (select all that apply)

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