# A.2A Domain and Range of Linear Functions

A.2A can be a tricky standard to teach. Texas Algebra 1 teachers are responsible for setting the stage for their students' foundation in domain and range. The topic not only reoccurs throughout Algebra 1, but also is a key concept across function types in Algebra 2.

I have found that teaching domain and range of continuous linear functions - especially those with a domain and range of all real numbers - is extremely abstract for many students and that a healthy dose of applied problems goes a long way to helping students developed a deeper conceptual understanding of domain and range.

Lucky for us, the SE tells us to do just that!

# Vertical Alignment

In Algebra 1, students need to be able to determine the domain and range of linear functions:
• from mathematical problems (continuous and discrete)
• from linear functions in applied situations (continuous and discrete)
• and represent domain and range using inequalities
The student expectation for this standard states that students are expected to "determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities;" TAC §111.39

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In Algebra 2, students will extend their knowledge of domain and range beyond linear, quadratic, and exponential functions (A.2A, A.6A, and A.9A respectively) and write the domain and range of many different function types.

In Algebra 2, students will build on representing domain and range using inequalities and add interval notation and set notation as possible representations of domain and range.

Algebra 1 students are not bringing a lot of previous knowledge about domain and range with them from 8th-grade math. They have studied basic 2-variable linear equations but will need a lot of support to develop a deep understanding of domain and range. Their limited experience with 2-variable linear equations is important to acknowledge, however, when developing domain and range application problems for students to interact with.

# Don't forget the Knowledge and Skills statement!

Don't forget to take a quick look at the Knowledge and Skills statement. In my opinion, it links much more directly to literally all the other TEKS under the A.2 umbrella that directly address formulating linear equations, inequalities, and systems.

However, the reminder about the process standards is key, especially when developing a deeply foundational concept like the domain and range of functions.

# So what should I teach?

## Domain and range from mathematical problems

• discrete linear graphs (scatterplot)

• continuous linear graphs with no endpoints

• continuous linear graphs with one endpoint

• continuous linear graphs with two endpoints

• domain and range from other representations such as tables, sets of points, and mapping diagrams (this is a great tie-in to A.12A, determining whether or not relations represent functions)

## Domain and range from applied situations

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• Continuous - variables such as time or gallons that are reasonable to measure in parts of units
• Discrete - variables such as computers or people that are only reasonable to count in discrete increments

# Short on time?

If you need a little help getting started this year and are interested in a complete unit, I offer a TEKS-aligned unit that covers all the function basics for Algebra 1 students. I developed it from the ground up with the TEKS at the forefront of the development process. Find it here.

# Disclaimer

Hi! I'm Allison, a curriculum writer and Texas native. I have extensively studied the secondary math TEKS throughout my career as an educator. While attending Texas A&M University-Corpus Christi to earn my M.S. in Curriculum and Instruction, I focused on learning as much as I could about interpreting the standards and developing standards-aligned resources grounded in research-based strategies.

Many teachers have excellent resources from their campus or district at their disposal. That is a wonderful thing! My goal is to deliver complementary information to help ease the burden on teachers.

The Math Beach TEKS guides are subject to my interpretation of the standards. As always, please continue to use your professional judgment and consult with your colleagues for clarification when needed.