Warm Up – Tuesday – 12/3 Rationalize the following: 4 3 7 2 4 1− 5

Fact to Remember 𝑖 2 =−1

Rationalizing Imaginaries 𝑖 ′ 𝑠 in the denominator are also a problem because 𝑖 is really a square root. We get rid of them the same way by multiplying by the conjugate over the conjugate.

Rationalizing Imaginaries If you can simplify initially, do it!

Rational Functions Rational functions are functions in fractional form. There is an inverse relationship between y and x, meaning as x gets bigger, y gets smaller.

Vertical Asymptotes A vertical asymptote is an imaginary vertical line that the rational function approaches but never touches. For 𝑦= 1 𝑥 there is a V.A. at 𝑥=0.

Horizontal Asymptotes A horizontal asymptote is an imaginary horizontal line. 𝑦=0 for the rational function 𝑦= 1 𝑥 .

Describe the transformations Parent Function: 𝑦= 1 𝑥 . 1. 𝑦= 1 𝑥+1 2. 𝑦= 1 𝑥 −3 3. 𝑦= 1 𝑥−2 +4

Graphing Basic Rational Functions Identify the transformations. Move your asymptotes to match.

Graphing Basic Rational Functions