Grapher

Using this virtual manipulative you may:

• Graph a function
• Trace a point along the graph
• Dynamically vary function parameters
• Change the range of values displayed in the graph
• Graph multiple functions
• Restrict the domain of a function
• Zoom in on a region of the graph

Graph a function

1. Enter a function into the function window using your keyboard and the buttons above the window.

   The buttons above the function window can be used to enter a fraction, an exponent, a square root, absolute value or parentheses. You may also use standard calculator notation for these.

2. Use the arrow keys on the keyboard to move the cursor back and forth in the function window.
3. Click on the Graph button to display the graph of the function you entered.

Trace a point along the graph

1. Check (turn on) the Trace check box at the bottom of the graph window.

A slider will appear below the graph window.

2. Click and drag the slider to move the trace point along the graph.

   You may also use the left and right keyboard buttons to "nudge" the slider by small increments.

Dynamically vary function parameters

The expression for functions you enter may include constants named a, b, and c. After graphing the function, these constants can be dynamically varied. To do so:

1. Click on the Parameters button.
2. Choose the constant to vary.
3. Drag the slider.

To change the range of each parameter:

1. Enter new values in the windows.
2. Click on the Apply button.

Change the range of values displayed in the graph

1. Click on the Window button.
2. Enter the maximum and minimum x and y values you want displayed in the graph.
3. Click on the Apply button.

Graph multiple functions

You may graph up to three functions in the graph window. To graph more than one function:

1. Click on the Functions button.
2. Click on the g(x) or h(x) button.
3. Enter your function as explained above.

You can express g(x) or h(x) in terms of previously defined functions. For example, enter f(x) = sin(x). Now let g(x) = xf(x). Try h(x) = 3f'(x)-2f"(x).

Restrict the domain of a function

1. Click the Functions button.
2. Select the function to restrict.
3. Click the Restrict Domain button.
4. Enter the minimum and maximum x values for the function.
5. Click Apply.

Zoom in on a region of the graph

Draw a rectangle around the region of the graph you want to zoom in on:

1. Click in one corner of the region.
2. Hold the mouse button down and move the cursor to the other corner of the region.
3. Release the mouse button

Restore the graph window to the original zoom setting by clicking on the Default Window button.