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Rational Functions

A rational function can have a variable like "x" in the numerator AND the denominator. When this happens, there are some special rules and properties to consider.

Graphing Rational Equations

         

The graph of the rational function \[y=\frac{ax-b}{-2x+c}\] is as shown above. If \(x_1=5\) and \(y_1=4,\) what is the value of \(a+b+c ?\)

Which of the following functions represents the above graph?

Which of the above graphs is represented by the function \[y=\frac{-x+9}{x-14} ?\]

Assuming that \(a=6\) and \(b=3,\) which of the following functions represents the above graph?

If the graphs of two functions \(y=f(x)\) and \(y=g(x)\) are as shown above, which of the following is the graph of the function \(\displaystyle y=\frac{f(x)}{g(x)}?\)

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