Algebra II Unit 11

Big Idea:

Graph and transform rational functions; inverse variation.

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

Focus TEKS

2A.6(G) analyze the effect on the graphs of f(x) = 1/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.6(H) formulate rational equations that model real-world situations

2A.6(I) solve rational equations that have real solutions

2A.6(J) determine the reasonableness of a solution to a rational equation

2A.6(K) determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation

2A.6(L) formulate and solve equations involving inverse variation

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 determine the horizontal and vertical asymptotes of rational functions
• I will graph a rational function
• I will create, solve and graph an equation involving inverse variation
• I will solve an equation involving combined variation
• I will describe transformations of the parent rational function and sketch the graphs
• I will identify the x-intercepts, y-intercepts, and asymptotes of transformations of the parent rational function

Essential Questions:

• How do you find the common denominator of a rational expression?
• Why do rational expressions need to have a defined domain?

Extra Information:

Adopted Textbook: Springboard - Algebra II Texas Edition

District Grading Policy

Texas Gateway Online Resource Center