Two-Dimensional Plots

There are several types of two-dimensional plots in Maple. They provide for the plotting of the graph of a function of one variable, of a data set, of a parametrically defined curve, and of an implicitly defined curve. Here are the most frequently used two-dimensional plotting commands.

plot

• To plot the graph of a function of one variable in the plane, use:

          plot(f(x),x=a..b);
  

  For example: plot(sin(x), x=0..Pi);.
• To plot the graphs of several functions of one variable on the same coordinate axes use:

          plot({f(x),g(x),...,h(x)},x=a..b);
  

  Notice that the functions are separated by commas and the list is enclosed in braces. For example: plot({sin(x),cos(x)}, x=0..Pi);

  
  

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  QUESTION 4: On a single Maple plot, print the graph of and its tangent line at the point over the interval . How many times does the tangent line touch or intersect the graph of f? What are the coordinates of these intersection points? (See the section below to learn how to print.)
  

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• To plot a curve defined parametrically by , use:

          plot([f(t),g(t),t=a..b]);
  

  For example, plot( [sin(t), cos(t), t=0..2*Pi] ); To plot several parametric curves on the same plot, pack several ``square brackets'' together inside of ``curly braces'':

  plot({ [t,t^2, t=-2..2], [1+t, 1+2*t, t=-1..1] });
  

  
  

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  QUESTION 5: Plot and print the parametrized curve and the tangent lines to the curve at and . (Hint: parametrize the tangent lines by where is the velocity vector to the curve evaluated at . )
  

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• To plot a data set of form use:

          plot([x1,y1,x2,y2,...xn,yn],x=a..b);
  

  Notice that the coordinates of the n points are written in order as a list of 2n entries separated by commas and enclosed in square brackets. For example, to plot three points: plot([-1,0, 1,0, 0,2], x=-1..1);

implicitplot

If a curve is defined implicitly by (k a constant), that is, the curve is the set of points in the domain that satisfy this equation, use:

        implicitplot(g(x,y) = k, x=a..b,y=c..d);

Example: implicitplot( x^2+y^2=1, x=-1..1, y=-1..1 );