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

2. Fact to Remember
𝑖 2 =−1

3. 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.

4. Rationalizing Imaginaries
If you can simplify initially, do it!

8. 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.

9. 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.

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

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

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

15. Graphing Basic Rational Functions