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Definition
A rational function is a function that is the ratio of two polynomials. In other words, it is a function of the form:
Summary
1. Key Features
- Domain: All real numbers except those that make the denominator Q(x)=0.
- Vertical Asymptotes: Occur where the denominator is 0 and the numerator is not.
- Holes: Occur if a factor is common to both numerator and denominator and cancels out.
- Horizontal or Oblique Asymptotes:
- Describe end behavior of the function.
- Based on the degrees of the numerator and denominator.
2. Graphing Rational Functions
- Plot asymptotes (vertical and horizontal/oblique).
- Identify intercepts by setting numerator or denominator equal to 0.
- Sketch the behavior near asymptotes and in various intervals.
3. Simplifying and Analyzing
- Factor both the numerator and denominator.
- Cancel common factors (which may indicate holes).
- Identify discontinuities (values excluded from the domain).
4. Applications
- Used in rate problems, physics (e.g., resistance in circuits), economics (e.g., cost per unit), and medicine (e.g., dosage vs. time).
- Model relationships where one quantity is inversely related to another.
5. Common Topics in Texts
- Performing operations: addition, subtraction, multiplication, division of rational expressions.
- Solving rational equations.
- Analyzing and interpreting real-world problems involving rational models.
Rational Functions Math Activities
This is a fantastic bundle which includes 10 activities with answer guides about Rational Functions. All our worksheets are completely editable so can be tailored for your curriculum and target audience.
Resource Examples
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Worksheets Activities Included
- Parent Graphs & Basic Transforms
- Holes vs Vertical Asymptotes
- Horizontal Asymptotes by Degree
- Slant (Oblique) Asymptotes via Division
- Full Sketch from Features
- Identify the Function from Graph Clues
- Sign Charts
- “Is it a Hole or an Asymptote?”
- Build from Asymptotes + Anchor Points
- Challenge Mix