U4 Rational Functions(KA/PRE/U4)

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Unit 4: Rational Functions

Reducing Rational Expressions to Lowest Terms

To reduce a rational expression, factor numerator and denominator and cancel common terms.

End Behavior of Rational Functions

The degrees of the numerator and denominator determine the end behavior (horizontal asymptotes or slant asymptotes).

Discontinuities of Rational Functions

Points where the denominator is zero cause vertical asymptotes or holes (removable discontinuities).

Graphs of Rational Functions

Let's visualize an example rational function: f(x) = (x² - 1) / (x - 2).

Modeling with Rational Functions

Rational functions are used to model rates, ratios, and problems with asymptotic behavior (ex: speed/time).

Multiplying and Dividing Rational Expressions

Multiply: Multiply numerators and denominators. Divide: Multiply by reciprocal of the divisor.

Adding and Subtracting Rational Expressions

Find common denominator, rewrite each term, then add or subtract numerators.

Quiz: Test Your Understanding

What type of discontinuity occurs when the denominator is zero but the factor cancels?

  1. Vertical asymptote
  2. Removable discontinuity (hole)
  3. Horizontal asymptote

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