Embedded Files
Lesson Video
Lesson Video
Focus Standards
Focus Standards
Learning Focus
Learning Focus
Additional Resources
Additional Resources
A Develop Understanding Task
A Develop Understanding Task
Introduces rational functions by examining key features of the graph . Develops understanding of vertical and horizontal asymptotes.
Introduces rational functions by examining key features of the graph . Develops understanding of vertical and horizontal asymptotes.
Understand the behavior of for very large values and for values near .
Graph and describe the features of using appropriate notation.
How can winning the lottery help us to think about ?
What features make mathematically interesting?
A Solidify Understanding Task
A Solidify Understanding Task
Builds on understanding of rational functions by transforming the graph of and by examining key features of the transformation. Focuses on using vertical and horizontal asymptotes to graph simple rational functions.
Transform the graph of .
Write equations from graphs.
Predict the horizontal and vertical asymptotes of a function from the equation.
What other functions can be made from ? What will their graphs look like?
A Solidify Understanding Task
A Solidify Understanding Task
Extends understanding of rational functions to more complex equations, and provides an opportunity to discover the relationship between the degree of the numerator and denominator and the horizontal asymptotes.
Define a rational function.
Explore rational functions, and find patterns that predict the asymptotes and intercepts.
What is a rational function? What does the graph of a rational function look like?
A Solidify Understanding Task
A Solidify Understanding Task
Formalizes the definition of rational functions. Develops procedures for rewriting rational functions when the degree of the numerator is greater than the degree of the denominator by connecting to rational numbers. Compares the graphs of equivalent functions to introduce holes and slant asymptotes.
NC.M3.A-APR.6
NC.M3.A-APR.7
NC.M3.A-APR.7.b
NC.M3.A-SSE.1.a
NC.M3.A-SSE.2
NC.M3.F-IF.7
Write equivalent rational expressions.
Find the features of rational functions with numerators that are one degree greater than the denominator.
What does the graph of a rational function look like if the function has common factors in the numerator and denominator?
What does the graph of a rational function look like if the degree of the numerator is greater than the degree of the denominator?
A Solidify Understanding Task
A Solidify Understanding Task
Continues the connection between rational numbers and rational expressions to teach operations on rational expressions (adding, subtracting, multiplying, and dividing).
Add, subtract, multiply, and divide rational expressions.
How are the operations performed on rational expressions like operations performed on rational numbers?
What ideas about fractions are revealed when we change forms?
A Practice Understanding Task
A Practice Understanding Task
Develops a strategy for and builds fluency in graphing rational functions by determining the behavior near the asymptotes.
Determine a process for graphing rational functions from an equation.
How can we quickly determine the behavior near the asymptotes of a rational function?
Video: Graphing rational functions
A Practice Understanding Task
A Practice Understanding Task
Models a situation using a rational equation, and applies work from previous lessons to solve equations that contain rational expressions.
NC.M3.A-APR.7.a
NC.M3.A-CED.1
NC.M3.A-REI.1
NC.M3.A-REI.2
NC.M3.A-SSE.1
NC.M3.A-SSE.1.a
NC.M3.A-SSE.1.b
Solve equations that contain rational expressions.
What real-life situations can be modeled with rational functions?
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