Algebra II Unit 2

Big Idea:

Graph absolute value and inverse functions; Operations of functions; Composition of functions

Student Expectations:

Priority TEKS

2A.7(I) write the domain and range of a function in interval notation, inequalities, and set notation

2A.2(A) graph the functions f(x)=√x, f(x)=1/x, f(x)=x³, f(x)= ³√x, f(x)=b^x, f(x)=|x|, and f(x)=log_b (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval

Focus TEKS

2A.2(B) graph and write the inverse of a function using notation such as f ^-1 (x) (algebraic linear functions and graphs)

2A.2(D) use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other

2A.6(C) analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d

Student Learning Targets:

• I will graph piecewise-defined functions and write domain and range of the function
• I will graph absolute value functions and describe the key attributes
• I will graph transformations of absolute value functions and describe the changes to the parent function
• I will explore the composition of two functions through a real-world scenario
• I will write the composition of two functions and evaluate the composition of two functions
• I will find the inverse of a function and write the inverse using proper notation
• I will use the composition of two functions to determine if functions are inverses of each other
• I will graph inverse functions and identify the symmetry

Essential Questions:

• How are composite and inverse functions useful in problem solving?
• How can you find the inverse of a relation or function?
• How can you determine whether the inverse of a function is a function?

Extra Information:

Adopted Textbook: Springboard - Algebra II Texas Edition

District Grading Policy

Texas Gateway Online Resource Center