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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 $$\displaystyle y=\frac{f(x)}{g(x)}?$$

graph6789

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