Algebra II Unit 12

Big Idea:

Simplify and solve rational expressions, equations, and inequalities.

Student Expectations:

Priority TEKS

2A.7(F) determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two

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

Student Learning Targets:

• I will simplify rational expressions
• I will multiply and divide rational expressions
• I will add and subtract rational expressions
• I will simplify complex fractions
• I will identify the vertical asymptotes of rational functions by finding the domain values that make the functions undefined.
• I will use the degrees of the numerator and denominator of rational functions to identify the horizontal asymptotes
• I will analyze and graph rational functions, identifying any asymptotes, intercepts, and holes
• I will solve rational equations, identifying any extraneous solutions
• I will solve rational inequalities by graphing
• I will solve rational inequalities by finding the sign of the inequality on either side of the numerator and denominator zeros

Essential Questions:

• How can you graph rational functions?
• What kinds of asymptotes may exist in rational functions and why?

Extra Information:

Adopted Textbook: Springboard - Algebra II Texas Edition

District Grading Policy

Texas Gateway Online Resource Center