Graphical Behavior: Holes - Clare-Gladwin RESD

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Graphical Behavior

Graphical Behavior

Holes

A hole is a point on the graph where the value of the function is not defined. If the numerator and denominator of a rational function have a common factor, they will cancel when simplifying. The cancelled value creates a hole in the graph. To determine the x -coordinate of a hole, set the cancelled factor equal to zero and solve. To determine the y -coordinate, plug the x -value into the simplified function and solve.

◀︎ Applications Jump to... Jump to... Overview Basic Operations Graphing Overview Transformations Domain and Range Composition of Functions Inverse Functions Post-Assessment: Families of Functions Multiple Choice Paper Post-Assessment: Families of Functions Multiple Choice Paper Post-Assessment: Families of Functions Multiple Choice Key Post-Assessment: Families of Functions Short Answer Post-Assessment: Families of Functions Short Answer Key Pre-Assessment: Polynomials Multiple Choice Paper Pre-Assessment: Polynomials Multiple Choice Paper Pre-Assessment: Polynomials Multiple Choice Key Overview Foundations Addition & Subtraction Multiplication Division Solving Applications Graphical Behavior End Behavior Quiz Finding Intercepts Zeros Quiz Modeling Addition and Subtraction Multiplication Division Post-Assessment: Polynomials Multiple Choice Paper Post-Assessment: Polynomials Multiple Choice Paper Post-Assessment: Polynomials Multiple Choice Key Post-Assessment: Polynomials Short Answer Post-Assessment: Polynomials Short Answer Key Pre-Assessment: Rationals Multiple Choice Paper Pre-Assessment: Rationals Multiple Choice Paper Pre-Assessment: Rationals Multiple Choice Key Overview Simplifying Rationals Multiplication Addition & Subtraction Solutions Applications Transformations Post-Assessment: Rationals Multiple Choice Paper Post-Assessment: Rationals Multiple Choice Paper Post-Assessment: Rationals Multiple Choice Key Post-Assessment: Rational Short Answer Post-Assessment: Rational Short Answer Key Pre-Assessment: Exponential & Logarithmic Functions Multiple Choice Paper Pre-Assessment: Exponential & Logarithmic Functions Multiple Choice Paper Pre-Assessment: Exponential & Logarithmic Functions Multiple Choice Key Overview Inverse Functions Properties Exponentials Logarithms Exponentials Logarithms Exponentials Compound Interest Quiz Logarithms Post-Assessment: Exponential & Logarithmic Functions Multiple Choice Paper Post-Assessment: Exponential & Logarithmic Functions Multiple Choice Paper Post-Assessment: Exponential & Logarithmic Functions Multiple Choice Key Post-Assessment: Exponential & Logarithmic Functions Short Answer Post-Assessment: Exponential & Logarithmic Functions Short Answer Key Pre-Assessment: Conics Multiple Choice Paper Pre-Assessment: Conics Multiple Choice Paper Pre-Assessment: Conics Multiple Choice Key Overview Completing the Square Circles Ellipses Hyperbolas Parabolas Applications Post-Assessment: Conics Multiple Choice Paper Post-Assessment: Conics Multiple Choice Paper Post-Assessment: Conics Multiple Choice Key Post-Assessment: Conics Short Answer Post-Assessment: Conics Short Answer Key Pre-Assessment: Univariate Data Multiple Choice Paper Pre-Assessment: Univariate Data Multiple Choice Paper Pre-Assessment: Univariate Data Multiple Choice Key Overview Variable Types Dot Plots Bar Graphs Histograms Box Plots Measures of Center Variation Control Charts Post-Assessment: Univariate Data Multiple Choice Paper Post-Assessment: Univariate Data Multiple Choice Paper Post-Assessment: Univariate Data Multiple Choice Key Post-Assessment: Univariate Short Answer Post-Assessment: Univariate Short Answer Key Pre-Assessment: Sequences & Series Multiple Choice Paper Pre-Assessment: Sequences & Series Multiple Choice Paper Pre-Assessment: Sequences & Series Multiple Choice Key Overview Pattern Building Arithmetic Arithmetic Sequence Geometric Geometric Sequence Other Arithmetic Arithmetic Series Geometric Geometric Series Summation Notation Summation Notation Post-Assessment: Sequences & Series Multiple Choice Paper Post-Assessment: Sequences & Series Multiple Choice Paper Post-Assessment: Sequences & Series Multiple Choice Key Post-Assessment: Sequences & Series Short Answer Post Assessment: Sequences & Series Short Answer Key Pre-Assessment: Probability & Counting Multiple Choice Paper Pre-Assessment: Probability & Counting Multiple Choice Paper Pre-Assessment: Probability & Counting Multiple Choice Key Overview Review Venn Diagrams Permutations & Combinations Pascal's Triangle Post-Assessment: Probability & Counting Multiple Choice Paper Post-Assessment: Probability & Counting Multiple Choice Paper Post-Assessment: Probability & Counting Multiple Choice Key Post-Assessment: Probability & Counting Short Answer Post-Assessment: Probability & Counting Short Answer Key Algebra II Final Exam Algebra II Final Exam Key Transformations ▶︎ Skip Table of contents

Table of contents

• Discontinuities
• Holes
  • Example 1
  • Ex 1 Graph
  • Example 2
  • Ex 2 Graph
  • Video Lesson
• Horizontal Asymptotes
  • Rule 2
  • Rule 3
• End Behavior
  • Example 2
  • Example 3
• Domain
  • Example 2
• Range
  • Video Lesson: Domain & Range
• Finding x-intercepts
  • Example 2
• Finding y-intercepts
  • Example 2
• Video Lesson: Graphing Rationals
  • More Graphing
• Guided Practice
• Practice
  • Answer Key
• Sources

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