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Rational Functions and Asymptotes

Graphing expressions with variables in the denominator and identifying vertical, horizontal, and slant asymptotes alongside points of discontinuity.

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Introduction to Rational Functions & Domain

Introduces the fundamental definition of a rational function, how to determine its domain, and identifies the concept of a point of discontinuity where the function is undefined.

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Curated flashcard stacks covering Rational Functions and Asymptotes.

Identifying Vertical Asymptotes
Focuses on the process of finding vertical asymptotes of rational functions. This involves factoring, simplifying, and identifying the roots of the remaining denominator.
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Identifying Vertical Asymptotes
Focuses on the process of finding vertical asymptotes of rational functions. This involves factoring, simplifying, and identifying the roots of the remaining denominator.
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Finding Slant (Oblique) Asymptotes
Focuses on the specific case where a rational function has a slant (or oblique) asymptote and details how to find its equation using polynomial long division or synthetic division.
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Finding Slant (Oblique) Asymptotes
Focuses on the specific case where a rational function has a slant (or oblique) asymptote and details how to find its equation using polynomial long division or synthetic division.
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Graphing Rational Functions: A Step-by-Step Guide
A comprehensive checklist to sketching the graph of a rational function by synthesizing all key features: intercepts, asymptotes, holes, and behavior analysis using test points.
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Graphing Rational Functions: A Step-by-Step Guide
A comprehensive checklist to sketching the graph of a rational function by synthesizing all key features: intercepts, asymptotes, holes, and behavior analysis using test points.
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Determining Horizontal Asymptotes
Explains the three rules for finding the horizontal asymptote of a rational function by comparing the degree of the numerator (n) to the degree of the denominator (m).
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Determining Horizontal Asymptotes
Explains the three rules for finding the horizontal asymptote of a rational function by comparing the degree of the numerator (n) to the degree of the denominator (m).
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Finding Holes (Removable Discontinuities)
Details the method for identifying and locating the coordinates of holes in the graph of a rational function, which occur when a factor in the numerator and denominator cancels out.
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Finding Holes (Removable Discontinuities)
Details the method for identifying and locating the coordinates of holes in the graph of a rational function, which occur when a factor in the numerator and denominator cancels out.
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Introduction to Rational Functions & Domain
Introduces the fundamental definition of a rational function, how to determine its domain, and identifies the concept of a point of discontinuity where the function is undefined.
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Introduction to Rational Functions & Domain
Introduces the fundamental definition of a rational function, how to determine its domain, and identifies the concept of a point of discontinuity where the function is undefined.
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