Algebra II Unit 10

Big Idea:

Graph and transform square root and cube root functions and find their inverses.

Student Expectations:

Priority TEKS

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

2A.4(F) solve quadratic and square root equations

2A.6(B) solve cube root equations that have real roots

2A.2(C) describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range

Focus TEKS

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

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.4(C) determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d

2A.4(E) formulate quadratic and square root equations using technology given a table of data

2A.4(G) identify extraneous solutions of square root equations

2A.6(A) analyze the effect on the graphs of f(x) = x³ and f(x) = ³√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

2A.7(G) rewrite radical expressions that contain variables to equivalent forms

2A.7(H) solve equations involving rational exponents

Ongoing TEKS

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

Student Learning Targets:

• I will graph and describe transformations of the square root function
• I will solve square root equations and identify extraneous solutions
• I will graph the transformations of the cube root function
• I will solve cube root equations and check the reasonableness of solutions
• I will graph and write the inverse of square root functions
• I will find the inverse relations of quadratic functions
• I will graph and write the inverse of cube root functions
• I will find the inverse relations of cubic functions

Essential Questions:

• How are expressions involving radicals and exponents related?
• How do power and radical functions model real-world problems and their solutions?

Extra Information:

Adopted Textbook: Springboard - Algebra II Texas Edition

District Grading Policy

Texas Gateway Online Resource Center