How to Graph Rational Expressions? (+FREE Worksheet!)

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Graphing Rational Expressions – Example 2:

Graph rational expressions. \(f(x)=\frac{3x}{x^2-2x}\)

Solution:

First, notice that the graph is in two pieces. Find \(y\)-intercept by substituting zero for \(x\) and solving for \(y (f(x)): x=0→y=\frac{3x}{x^2-2x}=\frac{3(0)}{(0^2-2(0)}=\frac{0}{0}\), \(y\)-intercept: None Asymptotes of \(\frac{3x}{x^2-2x}\): vertical: \(x=2\), Horizontal: \(y=0\) After finding the asymptotes, you can plug in some values for \(x\) and solve for \(y\). Here is the sketch for this function.

Exercises for Graphing Rational Expressions

Graph these rational expressions.

• \(\color{blue}{f(x)=\frac{x^2 -2x}{x-1}}\)

• \(\color{blue}{f(x)=\frac{x -5}{x^2-5x+1}}\)

• \(\color{blue}{f(x)=\frac{x^2}{4x-5}}\)

• \(\color{blue}{f(x)=\frac{5x-4}{2x^2-4x-5}}\)

• \(\color{blue}{f(x)=\frac{x^2 -2x}{x-1}}\)

• \(\color{blue}{f(x)=\frac{x -5}{x^2-5x+1}}\)

• \(\color{blue}{f(x)=\frac{x^2}{4x-5}}\)

• \(\color{blue}{f(x)=\frac{5x-4}{2x^2-4x-5}}\)

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