1. Today in Pre-Calculus No calculators needed Notes: –Rational Functions and Equations –Transformations of the reciprocal function Go over quiz Homework

2. Rational Functions A rational function, f(x), is a ratio or quotient of polynomial functions p(x) and q(x) expressed as * The domain of f(x) is all real numbers except where q(x) = 0

3. Rational Functions Are the following rational functions? If yes, state the domain. yes. D:(-∞,0) υ (0,∞) yes. D:(-∞,-2) υ (-2,2) υ (2,∞) No, numerator not a polynomial yes. D: (-∞,∞)

4. Transformations of the Reciprocal Function The simplest rational function is the basic function, Horizontal asymptote: y=0 Vertical asymptote: x=0

5. Example 1 Sketch the graph and find an equation for the function g whose graph is obtained from the reciprocal function, by a translation of 2 units to the right.

6. Example 2 Sketch the graph and find an equation for the function g whose graph is obtained from the reciprocal function, by a translation of 5 units to the right, followed by a reflection across the x-axis

7. Example 3 Sketch the graph and find an equation for the function g whose graph is obtained from the reciprocal function, by a translation of 4 units to the left, followed by a vertical stretch by a factor of 3, and finally a translation 2 units down.

8. Graphing Rational Functions The graph of any rational function of the form can be obtained by transforming by using polynomial long division.

9. Example 1 Vertical stretch: 3 Shift left 2

10. Example 2 Reflect across x-axis Shift up 2

11. Example 3 Vertical stretch: 8 Shift left 1 Shift down 3

12. Homework Pg. 245: 5-10 and 31-36 Chapter 2 test: Tuesday, November 25