## Reflection: Connection to Prior Knowledge Interval Notation - Section 3: Review of Basic Functions

As I work with determining the domain and range I find some students with a misconception of how to write the domain and range. One of the last topics discussed in Algebra 2 was rational expression. Some of the students have decided that the domain is x cannot equal a number. This error comes from just memorizing the idea that you find when the denominator is zero. What ever makes the denominator equal is not in your domain.

By looking at the graphs we can see that the graph of square root function has y-values at many x-values and is undefined at many x-values. I will ask how can we say that x does not equal something when it has a lot of point where it is undefined.

I also put up a rational function like f(x)=1/(x-1.  I ask about the domain and students say x does not equal 1.  I then say does it equal 2, .5, etc. I refer back to the definition and how the domain is representing what x-values the function can be. We should write the domain as x is all real numbers except x=1 to be precise.

When I observe errors like this I will discuss the observation with other teachers in the department. We discuss how as a department  we need to write the domain so we are precise. It is really easy for us to take shortcuts when we are discussing ideas.  When we work with students it is important that we are precise so students do not gain a misconception.

Error in reasoning with domain
Connection to Prior Knowledge: Error in reasoning with domain

# Interval Notation

Unit 2: Functions and Piecewise Functions
Lesson 1 of 15

## Big Idea: Explore the different methods of writing intervals in describing domains, ranges and intervals describing graphs.

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Standards:
Subject(s):
Math, Precalculus and Calculus, range, domain restrictions, 11th Grade, 12th Grade, interval notation, function, Mathematical literacy, function
60 minutes

### Katharine Sparks

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