'Slant asymptotes' diaporamas de présentation

PRECALCULUS I

PRECALCULUS I. Complex Numbers Real numbers + Imaginary numbers. Dr. Claude S. Moore Danville Community College. Definition of. The square root of a negative real number is not a real number. Thus, we introduce imaginary numbers by letting i =

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Section 3-7

Section 3-7. Graphs of Rational Functions. 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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Bellwork Find the inverse of the following functions

Bellwork Find the inverse of the following functions. d. Inverse Variation. Section 7.1. Classifying Direct and Inverse Variation. When two variables x and y show direct variation when y = ax for some nonzero constant a. Another type of variation is called inverse variation.

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Rational Function Discontinuities

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Rational Functions and Their Graphs

Rational Functions and Their Graphs. Section 2.6 Page 326. Definitions. Rational Function- a quotient of two polynomial functions in the form f(x) = p(x) q(x) ? 0 q(x) Domain:. Example 1. Find the domain of each rational function. Reciprocal Function.

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Consider the rational function below.

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2.6 Rational Functions

2.6 Rational Functions. Steps for Graphing guidelines. y-int. ( , ). 0. x-int. ( , ). none. let x = 0 to find y-int. Domain:. let y = 0 to find x-int.(s). where is g(x) undefined. Asymptote(s). if x is undefined at a number, there is a vertical asymptote

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9.3 Graphing General Rational Functions

9.3 Graphing General Rational Functions. p. 547. Steps to graphing rational functions. Find the y-intercept. Find the x-intercepts. Find vertical asymptote(s). Find horizontal asymptote. Find any holes in the function.

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9.3 Graphing General Rational Functions

9.3 Graphing General Rational Functions. p. 547. Steps to graphing rational functions. Find the y-intercept. Find the x-intercepts. Find vertical asymptote(s). Find horizontal asymptote. Find any holes in the function.

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Graphing Rational Functions

Graphing Rational Functions. What is a rational function?. or. Creating the graph. Put a vertical asymptote through the non-removable zeros of the denominator. (note: removable discontinuities get covered in calculus) Plot any horizontal or slant asymptotes.

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Factor the following completely:

3x 2 -8x+4 11x 2 -99 16x 3 +128. 4. x 3 +2x 2 -4x-8 2x 2 -x-15 10x 3 -80 . Factor the following completely:. (3x-2)(x-2). (x-2)(x+2) 2. (2x+5)(x-3). 11(x+3)(x-3). 16(x+2)(x 2 -2x+4). 10(x-2)(x 2 +2x+4). 9.3 Graphing General Rational Functions. p. 547.

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Strategy for Graphing Polynomials & Rational Functions

Strategy for Graphing Polynomials & Rational Functions. Dr. Marwan Zabdawi Associate Professor of Mathematics Gordon College 419 College Drive Barnesville, GA 30204 Office: (678) 359-5839 E-mail: mzabdawi@gdn.edu. Graphing Polynomials & Rational Functions.

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Rational Functions

Rational Functions. Section 2.6. Objectives. Determine the domain, x -intercepts, and y -intercepts of a rational function. Determine the vertical asymptotes (if any) of a rational function. Determine the horizontal asymptotes (if any) of a rational function.

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Slant Asymptotes

Slant Asymptotes. Slant asymptote. Occur when the degree of the numerator is one larger than the degree of the denominator To find: divide numerator by denominator and quotient is the SA. Find SA. Find SA of . Answer. Synthetic or long division. Finding asymptotes.

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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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