The CurveSketchSteps command is used to show how a student might plot a basic expression.

This command handles linear and quadratic polynomials in one variable, as well as single trig, log, 1/x and exponentials that are shifted and scaled. It does not support combinations of these functions and works best when the input is already simplified.

To avoid automatic simplifications the input expression can be given as a string. For example, calling CurveSketchSteps(cos(x-Pi/2)) will first evaluate cos(x-Pi/2) to sin(x) using normal Maple evaluation rules.  Instead, call CurveSketchSteps("cos(x-Pi/2"), to internally make use of InertForm:-Parse and avoid this simplification.

The displaystyle and output options can be used to change the output format.  See OutputStepsRecord for details.

This function is part of the Student:-Basics package.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right)\:$

$\mathrm{CurveSketchSteps}\left(2\sin \left(3x+\frac{\mathrm{\pi }}{3}\right)+1\right)$

$\begin{array}{lll}& & \text{Let's plot}2\sin \left(3x+\frac{\mathrm{\pi }}{3}\right)+1\\ \text{•}& & \text{Compared to the plot of}\sin \left(x\right)\text{, we have a vertical stretch by a factor of}2\\ & & 2\cdot \sin \left(3\cdot \left(x+\frac{\mathrm{\pi }}{9}\right)\right)+1\\ \text{•}& & \text{Then, we have a horizontal compression by a factor of}\frac{1}{3}\\ & & 2\cdot \sin \left(3\cdot \left(x+\frac{\mathrm{\pi }}{9}\right)\right)+1\\ \text{•}& & \text{Then, we have a vertical shift of}1\\ & & 2\cdot \sin \left(3\cdot \left(x+\frac{\mathrm{\pi }}{9}\right)\right)+1\\ \text{•}& & \text{Then, we have a horizontal shift of}-\frac{\mathrm{\pi }}{9}\\ & & 2\cdot \sin \left(3\cdot \left(x+\frac{\mathrm{\pi }}{9}\right)\right)+1\\ \text{•}& & \text{Apply the horizontal shift and stretch to the range,}x=-2\mathrm{\pi }..2\mathrm{\pi }\\ & & -2\mathrm{\pi }\cdot \left(\frac{1}{3}\right)+\frac{\mathrm{\pi }}{9}..2\mathrm{\pi }\cdot \left(\frac{1}{3}\right)+\frac{\mathrm{\pi }}{9}=\mathrm{-2.443460953}..1.745329252\\ \text{•}& & \text{We can now plot using the information extracted}\\ & & \mathrm{PLOT}\left(\mathrm{...}\right)\end{array}$

$\mathrm{CurveSketchSteps}\left(2x^2+4x+10\right)$

$\begin{array}{lll}& & \text{Let's plot}2x^2+4x+10\\ & & 2\cdot x^2+4\cdot x+10\\ \text{•}& & \text{Complete the square}\\ & & 2{\left(x+1\right)}^2+8\\ \text{•}& & \text{With the expression in vertex form we can extract valuable information}\\ & & 2\cdot {\left(x+1\right)}^2+8\\ \text{•}& & \text{The coefficient}2\text{of the}{\left(x+1\right)}^2\text{term indicates a parabola that opens}\text{up}\text{and has a vertical}\text{stretch}\text{of}2\\ & & 2\cdot {\left(x+1\right)}^2+8\\ \text{•}& & \text{We have a horizontal shift of}\mathrm{-1}\text{and a vertical shift of}8\text{which gives a vertex of (}\mathrm{-1}\text{,}8\text{)}\\ & & 2\cdot {\left(x+1\right)}^2+8\\ \text{•}& & \text{We can now plot using the information extracted}\\ & & \mathrm{PLOT}\left(\mathrm{...}\right)\end{array}$

$\mathrm{CurveSketchSteps}\left(4x+10\,\mathrm{output}=\mathrm{typeset}\right)$

$\begin{array}{lll}& & \text{Let's plot}4x+10\\ & & 4\cdot x+10\\ \text{•}& & \text{This is a line; find two points and draw a line through them}\\ & & y=4x+10\\ \text{•}& & \text{Set}x\text{= 0 to solve for y intercept}\\ & & y=10\\ \text{•}& & \text{This gives a y intercept of (0,}10\text{)}\\ & & y=10\\ \text{•}& & \text{Set expresson to 0 to solve for}x\text{intercept}\\ & & 0=4\cdot x+10\\ \text{•}& & \text{Rearrange expression}\\ & & 4\cdot x+10=0\\ \text{•}& & \text{Subtract}10\text{from both sides}\\ & & 4\cdot x+10-10=0-10\\ \text{•}& & \text{Simplify}\\ & & 4\cdot x=\mathrm{-10}\\ \text{•}& & \text{Divide both sides by}4\\ & & \frac{4\cdot x}{4}=\frac{\mathrm{-10}}{4}\\ \text{•}& & \text{Simplify}\\ & & x=-\frac{5}{2}\\ \text{•}& & \text{This gives an}x\text{intercept of (}-\frac{5}{2}\text{,0)}\\ & & x=-\frac{5}{2}\\ \text{•}& & \text{By connecting through the two points we can plot the line}\\ & & \mathrm{PLOT}\left(\mathrm{...}\right)\end{array}$

$\mathrm{CurveSketchSteps}\left(\frac{2}{3x+2}\,\mathrm{output}='\mathrm{link}'\right)$

The Student[Basics][CurveSketchSteps] command was introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.