Element pl-sketch: Sketching and annotating functions and curves

Questions below were designed to showcase the different features of pl-sketch.

This question is the example from the documentation of pl-sketch. It illustrates the basic functionalities of the element, including the use of different drawing tools, initial drawings, and grading criteria.

For full marks, draw the function $f(x) = 2^x$ (connecting the provided helper points) and mark the horizontal asymptote at $y = 0$.

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The element supports a variety of drawing tool types that can be added as needed for specific questions. See the element documentation for more details on the how each tool type can be used an graded.

Due to space limitations, a maximum of 7 tools (in addition to default buttons) can be placed in the element's toolbar. To organize elements or add more than 7 for the same question, dropdown groups can be used.

This question has no grading criteria, so any non-empty submission is considered correct.

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The drawing canvas itself can be customized by changing its display size and the visible x- and y-ranges inside the canvas. All drawings and the grid lines are scaled automatically.

This question also illustrates two other customizations: it is set up to allow blank submissions, and it prevents drawn objects from being dragged off-canvas. The latter setting is recommended when using object counts as grading criteria, because if students drag objects partially off-canvas, they might become hard to see for the human eye and can cause confusion.

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Drawings can be auto-graded based on different grading criteria, some of which are specific to certain drawing tool types. For tools like points and asymptote lines, common grading criteria are the number of placed objects per type and their position.

Note that unlike most other auto-graded elements, pl-sketch does not provide a sample solution in the answer panel as there might exist a wide range of solutions for a single question. We recommend using an image that is specific to that panel if a sample solution is needed.

This question requires exactly 3 points to be placed, of which 2 must be at the locations $(0,0)$ and $(1,1)$. The last point can be placed anywhere as long as its x-coordinate is less than 2 and its y-coordinate is in the interval $[-3,3]$.

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A common use case for the element is to draw and grade function sketches. The freehand drawing, spline and poly-line tool types are specifically designed for function sketching. Drawings as a single function, even if they consist of distinct segments or have small gaps. Submissions where multiple y-values exist for the same x-coordinate are marked as invalid to prevent ambiguities.

For this question, a function needs to to be drawn that is defined anywhere right of $x=-1$ and that matches $f(x) = x$ in the interval $x=[-1,1]$. It also must be monotonously increasing right of $x=1$.

All grading criteria can be customized, both to adjust tolerances, and to determine how special cases like definition gaps are handled. Furthermore, grading criteria can be weighted, and also staged to establish dependencies between grading criteria. The documentation describes the available settings and also lists more types of criteria, such as concavity checks or length-based grading.

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The element also supports drawing and auto-grading polygons, for example to shade regions of a graph. In this question, a triangular polygon should be drawn that covers the gap between the given functions in the interval $[0,2]$.

Note that polygon grading is computationally expensive and also somewhat limited. For example, it is not possible to directly compare a polygon's sides to functions. We recommend using approximations, such as a set of reference points that need to be covered by the polygon, instead.

Also note that students might draw overly complex shapes in an attempt to create a pixel-perfect solution, which is counter-productive as it slows down grading to the point where a submission becomes invalid. We strongly recommend giving students a low-stakes opportunity to practice all available drawing tools before using them in exams.

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Element pl-sketch: Sketching and annotating functions and curves

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Started at:
2026-08-04 22:42:51 (CDT)
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