Holt McDougal Algebra 2 Rational Functions Holt Algebra 2Holt McDougal Algebra 2 How do we graph rational functions? How do we transform rational functions.

Slides:

Advertisements

Similar presentations

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

Advertisements

9.3 Rational Functions and Their Graphs

Rational Expressions GRAPHING.

Graphs of Exponential and Logarithmic Functions

Rational Functions 8-4 Warm Up Lesson Presentation Lesson Quiz

Objective Transform polynomial functions..

TODAY IN ALGEBRA 2.0…  Review: Factoring polynomials  Learning Target: 8.2 You will graph rational functions  Independent Practice.

ACT Class Opener: om/coord_1213_f016.htm om/coord_1213_f016.htm

Rational Functions 4-2.

Function - 1 Meeting 2. Definition of Function.

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

Objectives Identify the multiplicity of roots.

Introduction to Rational Equations 15 November 2010.

POLYNOMIAL, RATIONAL, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS College Algebra.

Asymptote. A line that the graph of a curve approaches but never intersects. Add these lines to your graphs!

Lesson 2.6 Rational Functions and Asymptotes. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:

Exponential Functions MM3A2e Investigate characteristics: domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rate of.

Observer Professor Susan Steege

6.3 Logarithmic Functions. Change exponential expression into an equivalent logarithmic expression. Change logarithmic expression into an equivalent.

Find the zeros of each function.

Section 5.4 Logarithmic Functions. LOGARITHIMS Since exponential functions are one-to-one, each has an inverse. These exponential functions are called.

Essential Questions How do we use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation of least degree with given roots?

Essential Questions How do we identify the multiplicity of roots?

What is the end behavior?

I can graph a rational function.

Objective: Students will be able to graph rational functions using their asymptotes and zeros.

Holt McDougal Algebra 2 Fundamental Theorem of Algebra How do we use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation.

Radical Functions Essential Questions

Rational Functions Essential Questions

Warm Up Identify the domain and range of each function.

Holt McDougal Algebra 2 Radical Functions Graph radical functions and inequalities. Transform radical functions by changing parameters. Objectives.

Holt McDougal Algebra 2 Rational Functions Graph rational functions. Transform rational functions by changing parameters. Objectives.

Notes Over 4.2 Sketching Graphs of a Rational Function Steps in Graphing a Rational Function. 1.Find the vertical and horizontal asymptotes of the function.

Rational Functions Lesson Goals -recognize asymptotic presence -determine and locate vertical asymptotes -determine and locate horizontal asymptotes -graph.

How do we solve exponential and logarithmic equations and equalities?

Math – Exponential Functions

Notes Over 9.2 Graphing a Rational Function The graph of a has the following characteristics. Horizontal asymptotes: center: Then plot 2 points to the.

Check It Out! Example 2 Identify the asymptotes, domain, and range of the function g(x) = – 5. Vertical asymptote: x = 3 Domain: {x|x ≠ 3} Horizontal asymptote:

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

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

Chapter Rational Function. Objectives Graph rational functions. Transform rational functions by changing parameters.

Warmup 3-24 Simplify. Show work! Solve for x. Show work! 4. 5.

Holt Algebra Rational Functions The values of h and k affect the locations of the asymptotes, the domain, and the range of rational functions whose.

Summarize the Rational Function Task

Rational Functions and Their Graphs

The Natural Base, e Essential Questions

Rational Functions Essential Questions

Putting It All Together

6-8 Roots and Zeros – Day 1 SWBAT

Notes Over 11.8 Cross Multiplying

Summarize the Rational Function Task

MATH 1310 Section 5.1.

Attributes and Transformations of Reciprocal Functions

Radical Functions Essential Questions

Introduction to Rational Equations

Putting It All Together

Graph rational functions.

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

Rational Functions Essential Questions

Analysis Portfolio By: Your Name.

Domain, Range, Vertical Asymptotes and Horizontal Asymptotes

MATH 1310 Section 5.1.

Section 8.4 – Graphing Rational Functions

Graphing Simple Rational Functions

Students, Take out your calendar and your homework

Pre-Calculus 1.2 Kinds of Functions

Which is not an asymptote of the function

MATH 1310 Section 5.1.

Presentation transcript:

Holt McDougal Algebra 2 Rational Functions Holt Algebra 2Holt McDougal Algebra 2 How do we graph rational functions? How do we transform rational functions by changing parameters?

Holt McDougal Algebra 2 Rational Functions A discontinuous function is a function whose graph has one or more gaps or breaks. The hyperbola graphed in Example 2 and many other rational functions are discontinuous functions. A continuous function is a function whose graph has no gaps or breaks. The functions you have studied before this, including linear, quadratic, polynomial, exponential, and logarithmic functions, are continuous functions.

Holt McDougal Algebra 2 Rational Functions

Holt McDougal Algebra 2 Rational Functions Some rational functions, including those whose graphs are hyperbolas, have a horizontal asymptote. The existence and location of a horizontal asymptote depends on the degrees of the polynomials that make up the rational function. Note that the graph of a rational function can sometimes cross a horizontal asymptote. However, the graph will approach the asymptote when |x| is large.

Holt McDougal Algebra 2 Rational Functions

Holt McDougal Algebra 2 Rational Functions HA: VA: Graph the function (p < q). State the domain and range. x-intercepts: xy xy Domain: Range:

Holt McDougal Algebra 2 Rational Functions HA: VA: Graph the function (p < q). State the domain and range. zeros: xy xy Domain: Range:

Holt McDougal Algebra 2 Rational Functions HA: VA: Graph the function (p > q). State the domain and range. zeros: Diagonal asymptotes: xy xy Domain: Range:

Holt McDougal Algebra 2 Rational Functions HA: VA: Graph the function (p > q). State the domain and range. zeros: Diagonal asymptotes: xy xy Every y - line worth 2 Domain: Range:

Holt McDougal Algebra 2 Rational Functions HA: VA: Graph the function (p > q). State the domain and range. zeros: Diagonal asymptotes: xy xy Every line worth 2 Domain: Range:

Holt McDougal Algebra 2 Rational Functions HA: VA: Graph the function (p > q). State the domain and range. zeros: Diagonal asymptotes: xy xy Domain: Range:

Holt McDougal Algebra 2 Rational Functions HA: VA: Graph the function (p = q). State the domain and range. zeros: xy Domain: Range:

Holt McDougal Algebra 2 Rational Functions HA: VA: Graph the function (p = q). State the domain and range. zeros: xy xy Domain: Range:

Holt McDougal Algebra 2 Rational Functions Lesson 6.4 Practice C