3.5-RationalFunctions - Rational Functions and Their Graphs...

Info iconThis preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon
Rational Functions and Their Graphs Section 3.5 JMerrill,2005 Revised 08
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Why Should You Learn This? Rational functions are used to model and solve many problems in the business world. Some examples of real-world scenarios are: Average speed over a distance (traffic engineers) Concentration of a mixture (chemist) Average sales over time (sales manager) Average costs over time (CFO’s)
Background image of page 2
Introduction to Rational Functions What is a rational number? So just for grins, what is an irrational number? A rational function has the form ( ) ( ) ( ) p x f x q x where p and q are polynomial functions = A number that can be expressed as a fraction: A number that cannot be expressed as a fraction: , 2 π 5 , 3, 4.5 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Parent Function The parent function is The graph of the parent rational function looks like……………………. The graph is not continuous and has asymptotes 1 x
Background image of page 4
Transformations The parent function How does this move? 1 x 1 3 x +
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Transformations The parent function How does this move? 1 x 1 ( 3) x +
Background image of page 6
Transformations The parent function And what about this? 1 x 1 4 ( 2) x - -
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Transformations The parent function How does this move? 1 x 2 1 x
Background image of page 8
Transformations 2 1 x 2 1 2 x + 2 1 4 ( 3) x + - 2 1 ( 3) x -
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Domain Find the domain of 2 x 1 f(x) + = Denominator can’t equal 0 (it is undefined there) 2 0 2 x x + ≠ - ( 29 ( 29 Domain , 2 2, -∞ - ∪ - ∞ Think: what numbers can I put in for x????
Background image of page 10
You Do: Domain Find the domain of 2) 1)(x (x 1 - x f(x) + + = Denominator can’t equal 0 ( 29 ( 29 1 2 0 1, 2 x x x + + ≠ - - ( 29 ( 29 ( 29 Domain , 2 2, 1 1, -∞ - ∪ - - ∪ - ∞
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
You Do: Domain Find the domain of = + 2 x f(x) x 1 Denominator can’t equal 0 2 2 1 0 1 x x + ≠ ≠ - ( 29 Domain , -∞ ∞
Background image of page 12
Vertical Asymptotes At the value(s) for which the domain is undefined, there will be one or more vertical asymptotes. List the vertical asymptotes for the problems below. 2 x 1 f(x) + = 2 x =- 2) 1)(x (x 1 - x f(x) + + = 1, 2 x x = - = - = + 2 x f(x) x 1 none
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Vertical Asymptotes The figure below shows the graph of 2 x 1 f(x) + = The equation of the vertical asymptote is 2 x =-
Background image of page 14
Vertical Asymptotes Definition: The line x = a is a vertical asymptote of the graph of f(x) if ( 29 f x → ∞ or ( 29 f x → -∞ as x approaches “a” either from the left or from the right.
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 16
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/10/2009 for the course MATH 87765 taught by Professor Levitt during the Spring '09 term at New York Institute of Technology-Westbury.

Page1 / 41

3.5-RationalFunctions - Rational Functions and Their Graphs...

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online