Reflection: Vertical Alignment Discontinuity in Rational Functions - Section 1: Definitions


When I introduce the definition of a rational algebraic function, I'll always ask the class if they can recall the definition of a rational number.  Typically, I get something like "A number you can write as a fraction."  With a little prompting, we can quickly refine this to the following:

A rational number is a number that can be expressed as the ratio of two integers.

Now, I'll say, compare this to our definition of rational function:

A rational algebraic function is a function that can be expressed as the ratio of two polynomials.

What do you know?  They're almost identical!  This is a great opportunity to begin (or continue) helping students to understand that rational expressions form a system analogous to the rational numbers (HSA-APR.7).  I wouldn't take it much further today, but it's good to sow some seeds.

By the way, you'll probably have to remind the class of the definition of polynomial...

  Making Analogies
  Vertical Alignment: Making Analogies
Loading resource...

Discontinuity in Rational Functions

Unit 7: Rational Functions
Lesson 4 of 17

Objective: SWBAT use the structure of a rational equation to identify points of discontinuity.

Big Idea: Unlike polynomials, rational functions may be discontinuous. Blink and you'll miss it; there's just one point removed!

  Print Lesson
2 teachers like this lesson
Math, Graphing (Algebra), Algebra, Function Operations and Inverses, Algebra 2, master teacher project, rational function, asymptotes, discontinuity
  45 minutes
rat func discontinuous
Similar Lessons
Maximizing Volume - Day 1 of 2
12th Grade Math » Functioning with Functions
Big Idea: A classic maximization problem is used to investigate relative extrema.
Troy, MI
Environment: Suburban
Tim  Marley
Graphing Linear Functions Using Given Information
Algebra I » Graphing Linear Functions
Big Idea: Students calculate slope and y-intercept before graphing a linear function on a coordinate plane.
Washington, DC
Environment: Urban
Noelani Davis
SUPPLEMENT: Linear Programming Application Day 1 of 2
Algebra I » Systems of Equations and Inequalities
Big Idea: This lesson gives students the opportunity to synthesize what they have learned before they begin to create their own linear programming problems.
Boston, MA
Environment: Urban
Amanda Hathaway
Something went wrong. See details for more info
Nothing to upload