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

2. 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.

3. 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.

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

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

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

9. Graphing Basic Rational Functions

11. 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.

12. Examples:

13. Example 2:

14. Example 3: