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Section 4.8 : Rational Functions

Sketch the graph of each of the following functions. Clearly identify all intercepts and asymptotes.

1. \( \displaystyle f\left( x \right) = \frac{7}{{5x + 10}}\)
2. \( \displaystyle f\left( x \right) = \frac{{6 - x}}{{x - 3}}\)
3. \( \displaystyle f\left( x \right) = \frac{{8x + 6}}{{4 - 2x}}\)
4. \( \displaystyle f\left( x \right) = \frac{{ - 2}}{{{x^2} - 5x}}\)
5. \( \displaystyle f\left( x \right) = \frac{{x + 3}}{{{x^2} + 4x - 5}}\)
6. \( \displaystyle f\left( x \right) = \frac{2}{{{x^2} - x - 12}}\)
7. \( \displaystyle f\left( x \right) = \frac{{5{x^2} + 1}}{{2{x^2} - 32}}\)
8. \( \displaystyle f\left( x \right) = \frac{{{x^2} - 5x + 4}}{{{x^2} + 2x - 15}}\)