# Unit 8 + Activities: Radical Equations and Relationships - Texas Algebra 2            Subject
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Unit 8 Calendar + Resource Guide
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1. This curriculum bundle contains guided notes handouts, practice worksheets, reviews, mid-unit assessments, tests, concept organizers, and activities, all aligned to the Texas Algebra 2 state standards (TEKS).Documents are in PDF format. Editable versions of all forms of the mid-unit assessments and
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This unit and activities bundle extends students' knowledge of function transformations to square root functions y = (x), cubic functions y = x^3. and cube root functions y = ∛(x). Students will write equations of transformed functions and describe transformations including vertical stretch and compression, horizontal stretch and compression, vertical and horizontal translation, and reflection about the x-axis and y-axis.

This unit also introduces solving radical equations, including square root equations, cube root equations, and equations involving rational exponents. Students will identify extraneous solutions of square root functions.

Finally, students will build on their knowledge of inverse functions by finding and graphing the inverse of cubic, cube root, quadratic, and square root functions including domain restrictions when necessary.

Documents are in PDF format.

Editable versions of the mid-unit assessment and test are also included in .docx format for MS Word.

UNIT 8 INCLUDES THE FOLLOWING LESSONS:

Lesson 1: Transformations I

Students will:

• formulate the equation of transformed square root, cubic, and cube root functions
• describe single function transformations performed on y = (x), y = x^3, and y = ∛(x)

Lesson 2: Transformations II

Students will:

• formulate the equation of transformed square root, cubic, and cube root functions
• describe composite function transformations performed on y = (x), y = x^3, and y = ∛(x)

Students will:

• solve square root and cube root equations
• check for extraneous solutions

Lesson 4: Solving Equations with Rational Exponents

Students will:

• solve equations involving rational exponents

Lesson 5: Cubic-Cube Root Relationship

Students will:

• find the inverse of cubic and cube root functions algebraically
• graph inverse functions
• verify functions using the composition of functions

Students will:

• find the inverse of quadratic and square root functions algebraically, including domain restrictions
• graph inverse functions
• verify functions using the composition of functions

Lesson 7: Inverse Function Study

Students will:

• write and graph inverses of cubic, cube root, quadratic, and square root functions
• verify functions using the composition of functions
• describe and analyze the relationship between a function and its inverse using multiple representations

EACH LESSON CONTAINS THE FOLLOWING ELEMENTS:

All resources are in PDF format. Check out the preview for a detailed look!

• The Lesson Notes are designed for use as a note-taking guide combined with guided practice.

• Practice A and Practice B are suitable for use as in-class practice and homework. Two comparable forms are included for increased versatility.

• The Exit Ticket is designed for a quick concept check at the end of the class period.

• The Warm-Up is designed for next-day use to reinforce the previous day’s learning.

• One-page display versions of the exit ticket and warm-up are included. Display the PDF page on a screen for student viewing and have students record their responses on notebook paper or scratch paper to save on printing.

ADDITIONAL RESOURCES EXCLUSIVELY AVAILABLE IN UNIT 8 INCLUDE:

• 3 Concept Organizers offer a complementary alternative for note-taking or post-lesson concept reinforcement.

• The Mid-Unit Review (Forms A and B) provides an opportunity for students to practice the concepts they learned in the first part of the unit.

• The Mid-Unit Assessment (Forms A and B) may be used as a test, quiz, or daily assignment to meet the specific needs of your students. Editable versions of Forms A and B are included as a .docx file for MS Word.

• The Unit Review (Forms A and B) helps students focus on the key concepts studied throughout the unit.

• The Unit Test (Forms A, B, and C) comes in two comparable multiple-choice forms (A and B) and one free-response form (C). The test key includes TEKS alignment for each question to facilitate easy data analysis. Editable versions of Forms A and B are included as a .docx file for MS Word.

11 ACTIVITIES ARE ALSO INCLUDED IN THIS BUNDLE:

Please view the previews in the bundle section for more details.

STANDARDS:

2A.2B, 2A.2C, 2A.2D, 2A.4C, 2A.4F, 2A.4G, 2A.6A, 2A.6B, 2A.7H from the Algebra 2 Texas Essential Knowledge and Skills (TEKS)

HSA.REI.A.2, HSA.REI.B.11, HSF.BF.B.3, HSF.BF.B.4, HSF.BF.B.4a, HSF.BF.B.4b, HSF.BF.B.4d from Common Core State Standards (CCSS)

A note from Allison at Math Beach Solutions about standards alignment: This resource was designed from the ground up to provide ready-made resources for Texas teachers to implement to facilitate their students’ mastery of the Algebra 2 TEKS (Texas Essential Knowledge and Skills TAC §111.40). A considerable effort has been made to ensure the TEKS are addressed thoroughly, but these resources will reflect my understanding of the TEKS. As always, continue to use your professional judgment and experience when lesson planning.

Looking for a long-term homework solution? Check out Algebra 2 Skill Spirals Review Workbook for a year-long solution for homework, warm-ups, or tutorials session resources. It supports the Texas Algebra 2 TEKS, too!

Produce an invertible function from a non-invertible function by restricting the domain.
Verify by composition that one function is the inverse of another.
Solve an equation of the form 𝘧(𝘹) = 𝘤 for a simple function 𝘧 that has an inverse and write an expression for the inverse. For example, 𝘧(𝘹) =2 𝘹³ or 𝘧(𝘹) = (𝘹+1)/(𝘹–1) for 𝘹 ≠ 1.
Find inverse functions.
Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Total Pages
160 pages + keys
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