## 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

# Discontinuity in Rational Functions

Unit 7: Rational Functions
Lesson 4 of 17

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

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Standards:
Subject(s):
Math, Graphing (Algebra), Algebra, Function Operations and Inverses, Algebra 2, master teacher project, rational function, asymptotes, discontinuity
45 minutes

### Jacob Nazeck

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