What is the Graph Sketcher?

College Algebra Related Pages: 166 & 185 "Domain and Range"
College Algebra and Trigonometry Related Pages: 166 & 185 "Domain and Range"
Precalculus Related Pages: 103 "Domain and Range"

This activity allows you to view functions graphed on the coordinate plane.
Visually verify the domain and range of a function by plotting the function in Graph Sketcher. You can verify a range by plotting horizontal line(s) in the form of y=r where r is the range you obtained in analyzing the function. If your range is correct the function should not cross the horizontal line(s). Since the equation of a vertical line is not a function, a vertical line cannot be plotted so you cannot verify the domain in the same manner as how you can verify the range. However, it is still possible to estimate where the vertical line would be plotted on the graph. Again, the function should not cross that line.

How Graph Sketcher Works

This software graphs functions similarly to the way you would graph on paper. Axes are drawn, and a scale is set - based on the input in the range boxes. Next a table of x values between the two specified limits is generated, and then corresponding y values are calculated. Points are plotted, dots are connected, and the graph is displayed.

The main difference in the way the software works versus graphing by hand is the number of points plotted. Graphing by hand, you would probably plot 5 to 10 points and use our "math intuition" to connect the points appropriately. The computer plots many more points (depending on the x range, somewhere around 100) and connects the dots. This is how graphing calculators work, too.

This can lead to interesting behavior for certain functions. Polynomials like lines and parabolas will graph just as they should. Other functions, such as those for which x appears in a denominator, may have places on the graph where the computer has trouble plotting them correctly. This leads to the following moral:

If you see something unexpected on a graph,
always ask yourself if that behavior makes sense
mathematically before you accept it as correct.


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