Zeros+of+Polynomial+Functions(2)

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This section involves rational functions, most specifically their graphical behavior near the x-values excluded from the domain. In general, the domain of a rational function of x includes all real numbers except x-values that make the denominator zero. The graphs of rational functions include asymptotes. A vertical asymptote is a vertical imaginary line which the graph does not cross. Similarly, a horizontal asymptote is a horizontal imaginary line which the graph does not cross. A final type of asymptote, called a slant asymptote, is a slanted imaginary line over which the graph does not cross.



The above picture represents both vertical and horizontal asymptotes. One can see that there is a vertical asymptote and x=2 because the graph does not cross that line. One can also see that there is a horizontal asymptote and y=1.

The above picture displays another graph that contains asymptotes. This graph has a vertical asymptote and x=0. Also, this graph has a slant asymptote along the line y=x. As previously explained, the graph does not cross these imaginary lines.

We have a PowerPoint and an interactive website which will help better explain rational functions.

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Hope this isn’t making you irrational!

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This section focuses on nonlinear inequalities and the way in which one can solve polynomial inequalities. The simplest way to solve polynomial inequalities is to use a number line because a polynomial can change signs only between its zeros. Between two consecutive zeros, a polynomial must be entirely positive or entirely negative. This means that when the real zeros of a polynomial are put in order, they divide the real number line into intervals in which the polynomial has no sign changes. These zeros are the critical numbers of the inequality, and the resulting intervals are the test intervals for the inequality. To solve an inequality, on simply needs to test one value from each of the test intervals to determine whether the value satisfies the original inequality.

We have developed a PowerPoint to help you better understand nonlinear inequalities.

We have designed a quiz formulated for you success where you can harness the skills you have learned from these two WebPages.



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