'Vertical asymptotes' presentation slideshows

Pre-Calculus Midterm Exam Review

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Functions and equations

Functions and equations. Mr. Thauvette DP SL Mathematics. Graphs of Functions. The x -intercepts of a function are the values of x for which y = 0. They are the zeros (i.e., solutions, roots) of the function. The y -intercept of a function is the value of y when x = 0.

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Chapter 5 Graphs and the Derivative

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Jeporady

Jeporady. Transformations. Symmetry. Asymptotes. Functions. Sketching. 100. 100. 100. 100. 100. 200. 200. 200. 200. 200. Jeporady. 300. 300. 300. 300. 300. 400. 400. 400. 400. 400. 500. 500. 500. 500. 500. Transformations 100 Points.

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Warm up

Warm up. Describe the end behavior of: Graph the function Determine the interval(s) on which the function is increasing and on which it is decreasing. . Lesson 3-7 Graphs of Rational Functions. Objective: 1. To graph rational functions.

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Rational Functions and Models

Rational Functions and Models. 4.6. Identify a rational function and state its domain Identify asymptotes Interpret asymptotes Graph a rational function by using transformations Graph a rational function by hand (optional). Rational Function. A function f represented by

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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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Warm-up (4 m)

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Chapter 8: The Unit Circle and the Functions of Trigonometry

Chapter 8: The Unit Circle and the Functions of Trigonometry. 8.1 Angles, Arcs, and Their Measures 8.2 The Unit Circle and Its Functions 8.3 Graphs of the Sine and Cosine Functions 8.4 Graphs of the Other Circular Functions 8.5 Functions of Angles and Fundamental Identities

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ET 2.6: Find the domain.

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Short Run Behavior of Rational Functions

Short Run Behavior of Rational Functions. Lesson 9.5. Zeros of Rational Functions. We know that So we look for the zeros of P(x), the numerator Consider What are the roots of the numerator? Graph the function to double check. Zeros of Rational Functions.

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4.6 Graph of Other Trigonometric Functions

4.6 Graph of Other Trigonometric Functions. Vertical Asymptotes. What are the exact values. Graphing y = tan x. What happens at the undefined values There is a Vertical Asymptote. What is happening with the domain?. Graphing y = tan x.

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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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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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Limits of Functions and Continuity

Limits of Functions and Continuity. The Limit of a Function. The limit as x approaches a ( x ? a ) of f ( x ) = L means that as x gets closer and closer to a (on either side of a ), f ( x ) must approach L . Here, f ( a ) does not need to exist for the limit to exist. ?. ?.

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5.3

Limits Involving Infinity. 5.3. Bell work. Without a calculator, evaluate each limit either intuitively or with a table of values. If a limit approaches infinity it technically does not exist. Asking you to find any horizontal asymptotes is the same as asking you to find .

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5.4: More Trigonometric Graphs

5.4: More Trigonometric Graphs . TSW understand the graphs of tangent, cotangent, secant, and cosecant, their periodicity, and their transformations at an 85% mastery level as demonstrated by discussion and practice. Periodic Properties. Tangent and Cotangent have period ?:

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5.4 More Trig Graphs sec/ csc

5.4 More Trig Graphs sec/ csc. To graph the secant and cosecant functions, we use the reciprocal identities. (Take the reciprocal of the y-coordinates of the ordered pairs.). Vertical asymptotes are at the points where sinx and cosx = 0. . Ex Graph: . Ex Graph: .

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Graphing other Trig functions

Graphing other Trig functions . 4-6. Secant and cosecant. Graph the appropriate sine or cosine function Label the vertical asymptotes Start at each min/max and go up/down each asymptote. Example. Graph .

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Graphing other Trig functions

Graphing other Trig functions . 4-6. Secant and cosecant. Graph the appropriate sine or cosine function Label the vertical asymptotes Start at each min/max and go up/down each asymptote. Example. Graph .

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