4.10 Curve Sketching - Maple T.A. 10 Help

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4.10 Curve Sketching

Your instructor can ask that you sketch a curve as part of an assignment. Some example curve sketching questions are:

  • Graph one or multiple lines or curves.
  • Indicate which region represents the solution set (cases: single line or curve; multiple lines or curves).
  • Make the line solid or dashed to indicate whether the line is in the solution set.
  • Remove the portion of the line or curve that does not belong.
  • Use an open or closed circle to indicate whether the endpoints belong.
  • Add asymptotes to logarithmic and exponential curves.

The sketch board is a set of tools that can be used to create and/or operate on various sketch types. With each question, Maple T.A. automatically provides the appropriate set and number of drawing tools (buttons).

Basic Curve Sketching Tasks

Introduction

This section outlines the basic tasks you can perform to solve questions that involve curve sketching.

Graphing a Line

To graph a line:

  1. Click Draw a Line (). This enables you to plot points on the coordinate grid.
  1. Plot two points on the coordinate grid. After you plot two points on the grid, a line is drawn through these points.
  1. To change the line, you can move either of the two points anywhere on the grid. You can also move the entire line by clicking and dragging on the line.
  1. To delete the line, click Delete () and then click the object you want to delete.

Graphing a Parabola

To graph a parabola:

  1. Click Draw Parabola (). This enables you to plot points on the coordinate grid that can be moved to shape and position the parabola.
  1. On the coordinate grid, plot the vertex first followed by another point on the parabola.
  1. You can change the parabola by dragging either of the two points anywhere on the grid. This will stretch, compress, reflect, or translate the parabola.
  1. To delete the parabola, click Delete () and then click on the object you want to delete.

Indicating a Region of the Graph

To indicate which region on the graph represents the solution set:

  1. Click Choose Region (). This enables you to select a region on either side of a single line or select a region bounded by two lines.
  1. Click anywhere inside the region that represents the solution set to the problem. The region is automatically shaded.
  1. To delete this shaded region, click Delete () and then click anywhere in the shaded area that you want to delete.

Making Solid or Dashed Lines for a Graph

To use solid or dashed lines for a graph:

  1. Click Toggle Solid/Dashed (). This enables to you to switch between solid and dashed lines interchangeably.
  1. Click on a line. If the line was solid, then the entire line becomes dashed. To change the line back to solid, click the line again and it will revert back to its original state.
  1. To delete the solid or dashed line, click Delete () and then click on the line you want to delete.

Removing a Portion of a Line or Parabola

To remove a portion of a line or parabola:

1. Click Snip Left () or Snip Right (). These tools enable you to remove a portion to the left or right (respectively) of a location on the parabola.

2. Click on the portion of the parabola you want to keep. If you selected Snip Left in the previous step, the portion of the parabola to the left of your cursor is removed. Similarly, if you selected Snip Right in the previous step, the portion of the parabola to the right of your cursor is removed.

Removing a Portion of a Line or Parabola between Two Points

To remove a portion of a line or parabola between two points:

1. Click Snip Between (). This enables you to remove a portion of a parabola between two selected points.

2. Select two points on the parabola by clicking on them. A solid, green point indicates each selected location. The portion of the parabola between these two solid, green points is automatically removed.

Including or Excluding Endpoints

To indicate the position of endpoints on the graph:

  1. Click Toggle Filled/Hollow (). This enables you to toggle back and forth between filled (included) and open (excluded) endpoints.
  1. Click on the endpoint that you want to include or exclude. If the endpoint is filled (included), click on it to make it open (excluded). Similarly, if the endpoint is open (excluded), click on it to make it filled (included).

Graphing Absolute Values

To graph an absolute value:

  1. Click Draw Absolute Value (). This enables you to plot the vertex and an additional point on the coordinate grid.
  1. Plot the vertex first followed by an additional point on the grid. The absolute value graph is drawn automatically.
  1. You can change the absolute value graph by dragging either of the two points anywhere on the grid. This will stretch, compress, reflect, or translate the absolute value.
  1. To delete the absolute value graph, click Delete () and then click on the object you want to delete.

Graphing Exponential Curves

To graph an exponential curve:

  1. Click Draw Exponential (). This enables you to plot two points and a horizontal asymptote.
  1. Plot two points on the exponential curve.
  1. Plot the horizontal asymptote for the curve: Click the location on the coordinate grid where you want to place the horizontal asymptote. A dashed, horizontal line is automatically drawn through the point on the grid where you clicked. If you would like to move this horizontal asymptote, simply drag it to its new location.
  1. To delete the exponential curve, click Delete () and then click on the object you want to delete.

Graphing Logarithmic Curves

To graph a logarithmic curve:

  1. Click Draw Logarithmic (). This enables you to plot two points and a vertical asymptote.
  1. Plot two points on the logarithmic curve.
  1. Plot the vertical asymptote for the curve: Click the location on the coordinate grid where you want to place the vertical asymptote. A dashed, vertical line is automatically drawn through the point on the grid where you clicked. If you would like to move this vertical asymptote, simply drag it to its new location.
  1. To delete the logarithmic curve, click Delete () and then click on the object you want to delete.