1. Rational Functions, Transformations
Chapter 5 Functions
5.6
Rational Functions,
Transformations
MATHPOWERTM 11, WESTERN EDITION
5.6.1

2. x y Graphing the Basic Rational Function
A rational function is a function of the form
where g(x) and h(x) are polynomials and h(x) ≠ 0.
Graph x y
-10
-1/10 -2
-1/2 -1
undefined
1/2 2 1

3. Graphing the Basic Rational Function
The function is undefined
when x = 0. This shows up as an
asymptote.
Asymptote: a line that a curve
approaches but never touches.
Vertical asymptote: x = 0
Horizontal asymptote: y = 0
Asymptotes
Domain: x ≠ 0, x ϵ R.
Range: y ≠ 0, y ϵ R
5.6.7

4. Rational Functions and Transformations
Graph
Compare the graph of
with
Vertical stretch by a factor of 5, horizontal translation 2 units right.
Sketch the graph using transformations.
The horizontal asymptote is translated 2 units right as well.
Domain: x ≠ 2, x ϵ R.
Range: y ≠ 0, y ϵ R
5.6.7

5. Graphing Rational Functions
5.6.8

6. Compare Rational Equations
Consider
Describe how this function is related to f(x).

8. Assignment:
p. 442 #1, 3, 4a, 5b, 6, 7c, 8, 10, 13