MAT200
Franklin College
Erich Prisner

Second

MathCad Session

Range Variables and Tables

A range variable takes on many values. Type x:1;10 below your function definition---you will see x:=1..10. Now type x= and you see all x-values. Type f(x)= and you see all function values of the x-values (y-values). You can also change the increment. Replace your definition of the range variable x by  x:1,1.3;10 and see what happens. 

Plots

To plot a function f(x) from a to b, the function has to be defined already, and x has to be a range variable ranging (at least) from a to b with tiny increments (less than 0.1). MathCad creates a table of x- and y-values, plots these points, and connects them by straight lines. You type @, replace the middle placeholder at the bottom by x, the middle placeholder on the left by f(x). The other two bottom placeholder you replace by a and b, the boundaries for your plot.

Plotting multiple functions

Just replace the middle left placeholder by f(x),g(x),h(x) (provided all these functions are defined). You format a plot by double-clicking on it. You resize the plot region by drag-selecting it and moving the mouse until you see arrows (right and bottom). Then drag.

Exercises

Evaluating Functions

  1. Define a function f(x) = (x2-2x)/(x-1).
  2. Evaluate f(2).
  3. Evaluate f(1). What happens?
  4. Define a function g(x)=x-3
  5. Define x to be a range variable, going from 2 to 7
  6. Display x, f(x), g(f(x)), and f(g(x)) in tables. 
  7. Change x to be a range variable, going from 2 to 7 with increment 2 and see what happens.

Graphing Functions

  1. Define a function f(x) = (x2-2x)/(x-1).
  2. Graph f from -1 to 5 with increment 1.
  3. Change the increment to 0.3. What happens?
  4. Change the increment to 0.1 or even smaller, if you wish.

Graphing multiple functions

  1. Define the four functions
  2. Plot these four functions into a common coordinate system, with x from -1 and to 2, and with y between -1 and 4.
  3. What do you observe?
  4. Zoom in to check your conjecture.

Playing with linear functions

  1. On a new MathCad sheet, define the constants a:=1 and b:= 2. Also define the linear function f(x):=ax+b. Graph it between -3 and 5.
  2. Now play around by changing a and b and looking how the graph changes. Make sure you fully understand the meaning of a (slope) and b (y-intercept).

Point-Slope Formula

Create a MathCad sheet where you plug in the slope and one point, and which automatically computes the function through the point having this slope, and also displays it, with x between -3 and 5. 

Two-Point Formula

Create a MathCad sheet where you just have to give the coordinates of two points, and which automatically computes the formula of the linear function through both, and displays it with x between -3 and 5. 

Erich Prisner, August 2004