Example: f_{1}(x)=x^{2}
Click the "Graph" button (this button also refreshes the graph).
Functions can be traced either of two ways:
To see two functions graphed simultaneously:
Enter the second function f_{2}(x) in the text input field marked "f_{2}(x)=".
Click (to its "on" state) the check box next to this input field.
Click the "Graph" button.
A green point appears also on the graph of f_{2}(x) -- changing the value of c as above affects the green points on the graphs of both functions simultaneously.
Example: f_{1}(x)=x^{2} and f_{2}(x)=2-x
Up to two functions can be graphed and traced simultaneously.
To remove a function from the graph, click (to its "off" state) the check box next to the associated text input field and click the "Graph" button to refresh.
To erase the graph and all input fields, click the "Clear" button.
Line and Parabola:
f_{1}(x)=x^{2}
f_{2}(x)=2-x
Sine and Cosine:
f_{1}(x)=sin x
f_{2}(x)=cos x
The labels marked "f_{1}(c)=" and "f_{2}(c)=" give the values of the functions f_{1}(x) and f_{2}(x) when x=c, where c is the value given in the field marked "c=" (the horizontal position of the green points on the graph).
By using the tracing actions with the green
points on the graphs, it is possible to approximate and explore
intersection points of graphs.
To find such points more precisely, combine the tracing actions
with using the "Zoom In"
button under the graph.
All of the examples above have graphs
which intersect. In the
"Sine and Cosine" example
above, the graphs intersect at points corresponding to
values
c=/4,
3/4, 5/4, etc.