Warm Up – 12/4 - Wednesday Rationalize: 3 7 4 +1 4 3 + 2 4− 5

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

Identifying Asymptotes Vertical Asymptotes are where the denominator equals zero. Horizontal Asymptotes are given by 3 rules: If the degree of the numerator is greater than the degree of the denominator, there is not one. If the degree of the numerator is the same as the degree of the denominator, the horizontal asymptote is at the ratio of the leading coefficients. If the degree of the denominator is the greater than the numerator, H.A. at y = 0.

Examples:

Example 2:

Example 3: