### Continuity

Explores continuity of a function f (x) by comparing the value of the function at x=c to values of the function for x approaching c.
How to use   ||   Examples   ||   Other Notes

How to use
• Enter a function f (x) into the text input field marked "f (x)=". (Example: f (x)=x2)
• Click the "Graph" button (this button also refreshes the graph)
• Enter a value for c (Example: c=1) -- this can be done either of two ways:
• Enter the value directly into the text input field marked "c=", and click the "Graph" button.
• Use the mouse to click and drag the red point on the graph -- this point takes its horizontal position from the mouse position, and follows the graph of f (x); the horizontal position gives the value of c
• Enter a value for x (Example: x=2) -- this can be done either of two ways:
• Enter the value directly into the text input field marked "x=", and click the "Graph" button.
• Use the mouse to click and drag on the graph, anywhere except the position of the red point on the graph -- the horizontal position of the mouse, shown by the vertical blue line, gives the value of x.
• The "Point Zoom" button has an effect similar to the "Zoom In" button under the graph, but uses the red point on the graph as the center of the new graph region, so that the "Point Zoom" button requires only one mouse click, on the button itself, to enlarge the graph (unlike the "Zoom In" button, which requires a second click on the graph to determine the center point of the new graph region)
• To erase the graph and all input fields, click the "Clear" button
The text input field for f (x) can accept a wide variety of expressions to represent functions, and the buttons under the graph allow various manipulations of the graph coordinates. The text input fields for c and x can accept real numbers in decimal notation.
Examples
 Polynomial f (x)=x2 c=1, x=2 Exponential f (x)=ex c=0, x=1 Trigonometric f (x)=sin(x) c=0, x=1

Other Notes
The values of c and f (c) are indicated in the graph by orange lines, with the red point in the graph shown at the point (c,f (c)). The values of x and f (x) are indicated in the graph by blue lines. The table shows values of f (x) for x starting at the given value and approaching c -- in particular, the values x, c+(x-c)/2, c+(x-c)/4, etc. These values are indicated in the graph by green lines.