Problem:
Graphically, solve the inequality:

|x - 3| > |x + 4|

Visualization #1:
Graph each of the functions

f(x) = |x - 3| and g(x) = |x + 4|

and determine the part of the graph of f which is above the graph of g:

Using Derive:
  1. Prepare the program for graphics.
  2. If the first menu item is Algebra then press .
  3. Press for Author.
  4. Enter the first function
    abs(x-3)
  5. Enter the second function
    abs(x+4)
  6. Press twice to get the graph.
  7. Depending upon whether we had used graphics earlier, we may need to zoom in or out to get a better picture of the graph. To zoom out, press , press , change the direction to out, if necessary, by pressing the and now press .
  8. If necessary to zoom in or out some more, press as many times is needed to see a "complete" graph.
  9. By using the arrow keys, we can move a small cross to find an approximation to the intersections of the two graphs. The coordinates of the cross appear in the lower left hand corner of the screen.
Visualization #2:
Graph the function

f(x) = |x - 3| - |x + 4|

and determine the part of the graph of f which is above the x-axis:

Using Derive:
  1. Prepare the program for graphics.
  2. If the first menu item is Algebra then press .
  3. Press for Author.
  4. Enter the function
    abs(x-3) - abs(x+4)
  5. Press twice to get the graph.
  6. Depending upon whether we had used graphics earlier, we may need to zoom in or out to get a better picture of the graph. To zoom out, press , press , change the direction to out, if necessary, by pressing the and now press .
  7. If necessary to zoom in or out some more, press as many times is needed to see a "complete" graph.
  8. By using the arrow keys, we can move a small cross to find an approximation to the intersections of the two graphs. The coordinates of the cross appear in the lower left hand corner of the screen.