'Vertical asymptote' presentation slideshows

This is a 60 in 60 Challenge: 60 questions in 60 minutes

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ASYMPTOTES TUTORIAL

ASYMPTOTES TUTORIAL. Horizontal Vertical Slant and Holes. Definition of an asymptote. An asymptote is a straight line which acts as a boundary for the graph of a function.

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Rational Expressions/ Intro to Chaos

Rational Expressions/ Intro to Chaos. Macon State College Gaston Brouwer, Ph.D. July 2009. PART 1. Rational Expressions . Basics Simplifying Rational Expressions Rational Functions Horizontal & Vertical Asymptotes Graphing a Rational Function. Basics. Multiplying fractions:.

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Integration of irrational functions

Integration of irrational functions. Rational substitution is the usual way to integrate them. Ex. Evaluate Sol. Let then . Example. Ex. Evaluate Sol. Strategy for integration. First of all, remember basic integration formulae.

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Objectives for Section 3.3 Infinite Limits and Limits at Infinity

Objectives for Section 3.3 Infinite Limits and Limits at Infinity The student will be able to calculate infinite limits. The student will be able to locate vertical asymptotes. The student will be able to calculate limits at infinity. The student will be able to find horizontal asymptotes.

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Objectives for Section 10.3 Infinite Limits and Limits at Infinity

Objectives for Section 10.3 Infinite Limits and Limits at Infinity. The student will be able to calculate infinite limits. The student will be able to locate vertical asymptotes. The student will be able to calculate limits at infinity. The student will be able to find horizontal asymptotes. .

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Accurate Graphing and Unfamiliar Functions

Accurate Graphing and Unfamiliar Functions. Label your x-axis with the given interval Enter function into Y1 and set xmin and xmax to interval, zoom 0 Create a table of values and plot those points on your graph Find any relative extrema and plot on your graph

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Disappearing Asymptotes

Disappearing Asymptotes. The Visual Answers. Consider the graph of the function defined by:. Disappearing Asymptotes:. And then, the graph of the function defined by:. hole in the graph!. hole in the graph!. Again:.

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Exercises Graph the following functions. Solutions will follow the exercises.

Exercises Graph the following functions. Solutions will follow the exercises. Exercise Solutions The following graph solutions are done in blue. The asymptotes are done in red. 1. 2. Notice the difference in the equations of 1 and 2 and then compare the difference in the graphs of 1 and 2.

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1.5 Infinite Limits & Asymptotes

1.5 Infinite Limits & Asymptotes. After this lesson, you will be able to:. determine infinite limits from the left and from the right find and sketch the vertical asymptotes of the graph of a function. Suppose function.

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Unit 3 Review for Common Assessment

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GRAPHS OF OTHER TRIG FUNCTIONS

GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f ( x ) = tan x. Start with a "t" chart and let's choose values from our unit circle and find the tangent values. Tangent has a period of ? so it will repeat every ?. y. would mean there is a vertical asymptote here.

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Rational Functions

3.6: Rational Functions and Their Graphs. Rational Functions. Rational functions are quotients of polynomial functions. This means that rational functions can be expressed as

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Functions

Functions. AII.7 e 2009. Objectives: Find the Vertical Asymptotes Find the Horizontal Asymptotes. 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 .

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6.3 Logarithmic Functions

6.3 Logarithmic Functions. Change exponential expression into an equivalent logarithmic expression. Change logarithmic expression into an equivalent exponential expression. Domain of logarithmic function = Range of exponential function =.

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2.2 Limits Involving Infinity

Photo by Vickie Kelly, 2006. Greg Kelly, Hanford High School, Richland, Washington. 2.2 Limits Involving Infinity. North Dakota Sunset. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if:. or.

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Limits Involving Infinity

Photo by Vickie Kelly, 2006. Greg Kelly, Richland, Washington. Limits Involving Infinity. North Dakota Sunset. As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if:. or. This number becomes insignificant as .

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Logarithmic Functions

Logarithmic Functions . Categorized as Transcendental (Non-Algebraic) Functions Inverse of an Exponential Function Many real-life situations can be modeled using logarithmic functions, including: Earthquake Intensity Human Memory Pace of life in Large Cities.

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Infinite Limits

Infinite Limits. Lesson 2.5. Previous Mention of Discontinuity. A function can be discontinuous at a point The function goes to infinity at one or both sides of the point, known as a pole Example Enter this function into the Y= screen of your calculator Use standard zoom.

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1.6 Limits involving infinity

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