TEKS: Chapter 111. Mathematics See All Teacher Resources

111.40.c.6

(6) Cubic, cube root, absolute value and rational functions, equations, and inequalities. The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:

• (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;

• (B) solve cube root equations that have real roots;

• (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;

• (D) formulate absolute value linear equations;

• (E) solve absolute value linear equations;

• (F) solve absolute value linear inequalities;

• (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;

• (H) formulate rational equations that model real-world situations;

• (I) solve rational equations that have real solutions;

• (J) determine the reasonableness of a solution to a rational equation;

• (K) determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation; and

• (L) formulate and solve equations involving inverse variation.