'Oblique asymptote' presentation slideshows

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Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs. Does not exist. number. number. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs. Example:. Consider the function:. Study the behavior of the function around x=0. Vertical Asymptote.

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Rational Functions and Their Graphs Section 3.5

Rational Functions and Their Graphs Section 3.5. JMerrill,2005 Revised 08. 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)

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Properties of Rational Functions

Properties of Rational Functions. Learning Objectives. 1. Find the domain of a rational function 2. Find the vertical asymptotes of a rational function 3. Find the horizontal or oblique asymptotes of a rational function. Rational Function. To Find the Domain. Domain

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Section 4.1 Polynomial Functions

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Rational Functions

Rational Functions. Lesson 2.6, page 326. Objectives. Find domain of rational functions. Use arrow notation. Identify vertical asymptotes. Identify horizontal asymptotes. Use transformations to graph rational functions. Graph rational functions. Identify slant (oblique) asymptotes.

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Section 3.4

Section 3.4. Rational Functions. Rational Function. A rational function is a function of the form Where P and Q are polynomials and P(x) and Q(x) have no factor in common and Q(x) is not equal to zero. Consider . Find the domain and graph f . Solution:

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Chapter 4: Rational, Power, and Root Functions

Chapter 4: Rational, Power, and Root Functions. 4.1 Rational Functions and Graphs 4.2 More on Graphs of Rational Functions 4.3 Rational Equations, Inequalities, Applications, and Models 4.4 Functions Defined by Powers and Roots

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3.4 Rational Functions and Their Graphs

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Rational Functions and Their Graphs

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RATIONAL

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Graphing Rational Functions Example #3

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Translate

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2.6 Rational Functions and Their Graphs

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RATIONAL

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2. Solve for f(x) = k where k is the y-value of the asymptote.

From the previous section, we know the graph of the function can never cross the vertical asymptotes. However, this is not true for some functions with horizontal asymptotes. Below are examples of some functions whose graph does intersect the horizontal asymptote.

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AP Calculus AB

AP Calculus AB. Day 7 Section 3.5. Limits at Infinity. NOTE: f(x) may cross horizontal asymptotes near zero. Theorem:. Divide top & bottom by x to the highest power in the denominator. This means the function has an oblique asymptote.

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Slant Asymptotes

Slant Asymptotes. Consider a rational function whose denominator is of degree 1 or greater. If the degree of the numerator is exactly one more then the degree of the denominator, the graph of the function has a slant (or oblique) asymptote For example, the graph of. has a slant asymptote.

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Introducing Oblique Asymptotes

Introducing Oblique Asymptotes. Horizontal Asymptote Rules: If numerator and denominator have equal highest power, simplified fraction is the H.A. If denominator has a higher power than the numerator the H.A. is zero What happens when the numerator has a higher power than the denominator?.

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