There are two ways to find the roots of a funtion, using GRAPH/TRACE and using GRAPH/MATH/ROOT. These procedures are illustrated below:
Find the roots of the polynomial funtion f(x) = x3 + 2x2 - 3x - 6
- Graph the function (see Graphing Functions);
The graph is shown below in the standard window. We will use GRAPH/TRACE to
find the left most root
- choose the TRACE option (F4) in the GRAPH menu;
- keep pressing the left arrow to move the trace cursor to the left most root
as indicated by the red dot in the graph above.
- to get a more accurate view of the graph around this point choose
GRAPH/ZOOM/ZIN. Do this a couple times and we see that there are two roots
very close together.
Get back in trace mode with GRAPH/TRACE.
- use the left or right arrow keys to located the left most root (we want the x coordinate of the point whose y-coordinate is 0.) If the y-coordinates are never exactly 0 you can Zoom in more to get a more accurate value for the root. You should have found that the left most root is -2.
- Choose the GRAPH/MATH/ROOT option (you will need to press the MORE key to
display the MATH option in the GRAPH menu;
- This puts you in trace mode. You are being prompted to enter three
points:
- one to the left of the root;
- one to the right of the root; and
- a point close to the root.
One way to do this is to use the left or right arrow keys to move the trace cursor to the left of the root and press ENTER. Now move the cursor to the right of the root (the sign of the y-coordinate should change) and press enter. Finally, move the cursor as close as you can to the root and press enter. The root will be displayed at the bottom of the display. In this case you will get either -2 or -1.732050808, since we have two roots that are very close together. It is best to Zoom in on roots like this one to see if there are more than one and to help locate the one you are trying to find.
Find the right most root.
Find the roots of the absolute value funtion f(x) = |2x - 5|
Find the roots of the rational funtion f(x) =
Find the roots of the radical funtion f(x) =
Find the roots of the logarithmic funtion f(x) =
Find the roots of the exponential funtion f(x) =