2.6 Section 2.6.

Slides:

Advertisements

Similar presentations

9.3 Rational Functions and Their Graphs

Advertisements

Functions AII.7 e Objectives: Find the Vertical Asymptotes Find the Horizontal Asymptotes.

SECTION 3.2 RATIONAL FUNCTIONS RATIONAL FUNCTIONS.

Rational Expressions, Vertical Asymptotes, and Holes.

Rational Expressions GRAPHING.

A rational function is a function of the form: where p and q are polynomials.

Section 5.2 – Properties of Rational Functions

RATIONAL FUNCTIONS 2.6. RATIONAL FUNCTIONS VERTICAL ASYMPTOTES  To find vertical asymptotes first reduce the function if possible.  Set the denominator.

Objectives: Find the domain of a Rational Function Determine the Vertical Asymptotes of a Rational Function Determine the Horizontal or Oblique Asymptotes.

ACT Class Openers:

1 Find the domains of rational functions. Find the vertical and horizontal asymptotes of graphs of rational functions. 2.6 What You Should Learn.

Limits at Infinity Explore the End Behavior of a function.

9.3 Rational Functions and Their Graphs Rational Function – A function that is written as, where P(x) and Q(x) are polynomial functions. The domain of.

9.3 Graphing Rational Functions Algebra II w/ trig.

2.6 Rational Functions and Asymptotes 2.7 Graphs of Rational Functions Rational function – a fraction where the numerator and denominator are polynomials.

Class Work Find the real zeros by factoring. P(x) = x4 – 2x3 – 8x + 16

1 Warm-up Solve the following rational equation.

Bellwork 2. Find all zeros of the function, write the polynomial as a product of linear factors. 1. Find a polynomial function with integer coefficients.

Start Up Day 14 WRITE A POLYNOMIAL FUNCTION OF MINIMUM DEGREE WITH INTEGER COEFFICIENTS GIVEN THE FOLLOWING ZEROS:

Section 9-1 Graphing Rational Functions. Def: A rational function is of the form Where p(x) and q(x) are rational polynomials and The line that the graph.

Rational Functions A function of the form where p(x) and q(x) are polynomial functions and q(x) ≠ 0. Examples: (MCC9-12.F.IF.7d)

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

Finding Asymptotes Rational Functions.

Pre Calc Chapter 2 Section 6. Rational Functions Functions with the independent variable on the bottom of a fraction f(x) = N(x) D(x) Where N(x) & D(x)

 Review:  Graph: #3 on Graphing Calc to see how it looks. › HA, VA, Zeros, Y-int.

Removable Discontinuities & Vertical Asymptotes

1 Warm-up Solve the following rational equation.

Solving for the Discontinuities of Rational Equations 16 March 2011.

Lines that a function approaches but does NOT actually touch.

GRAPHING RATIONAL FUNCTIONS. Warm Up 1) The volume V of gas varies inversely as the pressure P on it. If the volume is 240 under pressure of 30. Write.

Graphing Rational Functions Day 3. Graph with 2 Vertical Asymptotes Step 1Factor:

Lesson 21 Finding holes and asymptotes Lesson 21 February 21, 2013.

GRAPHING SIMPLE RATIONAL FUNCTIONS. Investigation Graph the following using the normal window range. Draw a rough sketch of these functions on the back.

Rational Functions…… and their Graphs

Ch. 2 – Limits and Continuity

Simplifying Rational Expressions

Graphing Rational Functions

Rational Functions (Algebraic Fractions)

8.2 Rational Functions and Their Graphs

Rational functions are quotients of polynomial functions.

Ch. 2 – Limits and Continuity

Graphing Polynomial Functions

Horizontal Asymptotes

The Parent Function can be transformed by using

Warm UP! Factor the following:.

Asymptotes Rise Their Lovely Heads

Warm-up Solve the following rational equation..

Rational Function Discontinuities

Section 5.2 – Properties of Rational Functions

MATH 1310 Section 4.4.

RATIONAL FUNCTIONS A rational function is a function of the form:

Graphing Rational Functions

Simplifying rational expressions

5-Minute Check Lesson 3-7.

Simplifying rational expressions

Asymptotes Horizontal Asymptotes Vertical Asymptotes

2.6 Rational Functions and Their Graphs

Graphing Rational Expressions

Domain, Range, Vertical Asymptotes and Horizontal Asymptotes

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

Section 8.4 – Graphing Rational Functions

Rational Functions A rational function f(x) is a function that can be written as where p(x) and q(x) are polynomial functions and q(x) 0 . A rational.

EQ: What other functions can be made from

Copyright ©2015 Pearson Education, Inc. All right reserved.

Properties of Rational Functions

Solving and Graphing Rational Functions

December 15 No starter today.

Domain of Rational Functions

MATH 1310 Section 4.4.

Presentation transcript:

2.6 Section 2.6

Rational Functions and Asymptotes A rational function is a function written in the form of a polynomial divided by a polynomial. Domain: is the x-values Remember you cannot have a zero in the denominator of a fraction

Rational Functions and Asymptotes Vertical Asymptotes: To find the vertical asymptotes set the denominator equal to zero and solve for x. Horizontal Asymptotes: To find the horizontal asymptotes compare the degree of the numerator to the degree of the denominator.

Rational Functions and Asymptotes Horizontal Asymptotes: If the degree of the numerator is bigger than the degree of the denominator, then there is not a horizontal asymptote. If the degree of the numerator and the degree of the denominator are the same, then the horizontal asymptote is y = leading coefficient over leading coefficient.

Rational Functions and Asymptotes Horizontal Asymptotes If the degree of the denominator is bigger than the degree of the numerator, then the horizontal asymptote is y = 0 Asymptotes are equations: Vertical Asymptotes are x = # Horizontal Asymptotes are y = #