Part 7: Graphing Functions

1. Let's plot 3 sin(2x) over the interval [0,2π]. First we need to make sure x is unassigned. Enter
   x
   to check.  If Maple says that x has an assigned value, then remove it.  Now type
   3*sin( 2*x )
   Use your mouse to highlight this expression, click the right mouse button, and select "Plots"  > "Plot Builder" from the popup menus.  Make sure the first text box says "Plot" and the second box says "2-D plot".  Down below that it should say "x Axis", then "x" and then two boxes with numbers in them.  In the first box enter "0" and in the second box enter "2*Pi".  (If you leave out the asterisk or forget to capitalize the P it will not work.) When you click the "Plot" button Maple should make an arrow pointing from your formula to its plot.  (Note that Maple may switch to Text mode without warning after the plot.)
   
   We can obtain the same result by defining the function f given by
   f(x) = 3 sin(2x) and plotting f(x). Enter the following:
   f := x -> 3*sin(2*x)
   and
   f( x )
   Use the popup menus to plot this function over the interval [0,2π].

2. When the plot appears, use your mouse to "select" it -- you should see a box around the graphic. Experiment with the drag buttons at the corners and sides of the box. Experiment with the icons at the top of the screen to see what they do. In particular, obtain each of the following:
• A plot with no axes
• A plot with dots instead of a solid curve
• A boxed plot
• A plot with the appropriate aspect ratio, i.e., the horizontal units are the same as the vertical units.
  
  
• A "zoomed-in" version of the plot.
  
  
• A "zoomed-out" version of the plot.
  
  
• A view of just the left-hand part of the plot.
  
  
• A view of just the bottom part of the plot.
  

3. You can also use your right-hand mouse button to change the plot.  Experiment with the popup menus to see what they do.  In particular, obtain each of the following:
   
   
   • A plot with a dashed line instead of a solid curve.
     
     
   • A plot with a green curve instead of a red one.
     
   
   
   
4. Next we plot data given as ordered pairs. To do this we need the pointplot command in the Plots package.  First we need to load the plots package.  From the menu bar at the very top of the Maple window select "Tools" > "Load Package" > "Plots".  Maple should give you the message
   Loading plots
   (You may click on the underlined link if you want to see a list of commands in the Plots package.)
   Enter
   data:=[[0,1],[2,2],[4,6],[5,1]]
   Then enter
   pointplot(data)
   to see the plot.
   
   
5. Often we wish to view several graphs at the same time. One way to do this is directly with the popup menus.  Type
   sin(x), cos(x)
   Use your mouse to highlight this expression, click the right mouse button, and select "Plots"  > "Plot Builder" from the popup menus.  Make sure the first text box says "Plot" and the second box says "2-D plot".   Set the x axis and click "Plot" as before.
   
   
6. Another way to create multiple plots is to construct the plots separately and copy-and-paste them onto the same axes. Enter
   sin(x)
   and use the popup menus to plot it over the interval [0,2π].  Do the same for 
   cos(x)
   but change it to a different color.  Then use your mouse to copy and paste the cosine curve onto the sine curve.