| (E) determine the reasonableness of a solution to a
logarithmic equation.
(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.
(7) Number and algebraic methods. The student applies
mathematical processes to simplify and perform operations on expressions
and to solve equations. The student is expected to:
(A) add, subtract, and multiply complex numbers;
(B) add, subtract, and multiply polynomials;
(C) determine the quotient of a polynomial of degree
three and of degree four when divided by a polynomial of degree one
and of degree two;
(D) determine the linear factors of a polynomial function
of degree three and of degree four using algebraic methods;
(E) determine linear and quadratic factors of a polynomial
expression of degree three and of degree four, including factoring
the sum and difference of two cubes and factoring by grouping;
(F) determine the sum, difference, product, and quotient
of rational expressions with integral exponents of degree one and
of degree two;
(G) rewrite radical expressions that contain variables
to equivalent forms;
(H) solve equations involving rational exponents; and
(I) write the domain and range of a function in interval
notation, inequalities, and set notation.
(8) Data. The student applies mathematical processes
to analyze data, select appropriate models, write corresponding functions,
and make predictions. The student is expected to:
(A) analyze data to select the appropriate model from
among linear, quadratic, and exponential models;
(B) use regression methods available through technology
to write a linear function, a quadratic function, and an exponential
function from a given set of data; and
(C) predict and make decisions and critical judgments
from a given set of data using linear, quadratic, and exponential
models.
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