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College Algebra Related Pages: 378 "Properties of Logarithms" Verify properties of logarithms by plotting both the function before and after applying the properties. For example, plot the function f(x)=ln(3x) + ln(5x) and plot the function f(x)=ln(15x2) to see they are the same functions. (Note that the property applied here is logaxy = logax + logay.)
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:
always ask yourself if that behavior makes sense mathematically before you accept it as correct.
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