Refer to the TAKS information Booklet
Mathematics Grades 8-11 for a more complete

description of the objectives measured.

**Objective 1:The students will describe functional
relationship in a variety of ways.**

A(b)(1)** Foundations for functions .**The student understands that a
function re presents a dependence

of one quantity on another and can be described in a variety of ways.

(A) The student describes independent and dependent quantities in functional
relationships.

(B) The student [gathers and record data, or] uses data sets, to determine
functional

(systematic) relationships between quantities.

(C) The student describes functional relationships for given problem situations
and writes

equations or inequalities to answer questions arising from the situations.

(D) The student represents relationships among quantities using [concrete]
models, tables,

graphs, diagrams, verbal descriptions, equations, and inequalities.

(E) The student interprets and makes inferences from functional relationships.

**Objective 2:The students will demonstrate an
understanding of the properties and attributes of **

functions.

A(b)(2)**Foundations for functions .** The student uses the properties and
attributes of functions.

(A) The student identifies [and sketches] the general forms of linear (y = x)
and quadratic

(y = x^{2} ) parent functions.

(B) For a variety of situations, the student identifies the mathematical domains
and ranges and

determines reasonable domain and range values for given situations.

(C) The student interprets situations in terms of given graphs [or creates
situations that fit given

graphs].

(D) In solving problems, the student [collects and] organizes data, [makes and]
interprets

scatterplots, and models, predicts, and makes decisions and critical judgments.

A(b)(3) **Foundations for functions . **The student understands how algebra
can be used to express

generalizations and recognizes and uses the power of symbols to represent
situations.

(A) The student uses symbols to represent unknowns and variables .

(B) Given situations, the student looks for patterns and represents
generalizations algebraically.

A(b)(4) **Foundations for functions . **The student understands the
importance of the skills required to

manipulate symbols in order to solve problems and uses the necessary algebraic
skills required to

simplify algebraic expressions and solve equations and inequalities in problem
situations.

(A) The student finds specific function values, simplifies polynomial
expressions, transforms and

solves equations, and factors as necessary in problem situations.

(B) The student uses the commutative, associative, and
distributive properties to simplify

algebraic expressions.

**Objective 3:The student will demonstrate an
understanding of linear functions .**

A(c)(1)** Linear functions.** The student understands that linear functions
can be represented in different

ways and translates among their various representations.

(A) The student determines whether or not given situations can be presented by
linear functions.

(C) The student translates among and uses algebraic, tabular, graphical, or
verbal descriptions

of linear functions.

A(c)(2) ** Linear functions. **The student understands the meaning of
the slope and intercepts of linear

functions and interprets and describes the effects of changes in parameters of
linear functions in

real-world and mathematical situations.

(A) The student develops the concepts of slope as a rate of change and
determines slopes from

graphs, tables, and algebraic expressions.

(B) The student interprets the meaning of slope and intercepts in situations
using data, symbolic

representations, or graphs.

(C) The student investigates, describes, and predicts the effects of changes in
m and b on the

graph of y = mx + b.

(D) The student graphs and writes equations of lines given characteristics such
as two points , a

point and a slope, or a slope and -intercept.

(E) The student determines the intercepts of linear functions from graphs,
tables, and algebraic

representations.

(F) The student interprets and predicts the effects of changing slope and
-intercept in applied

situations.

(G) The student relates direct variation to linear functions and solves problems
involving

proportional change.

**Objective 4: The student will formulate and use linear
equations and inequalities.**

A(c)(3) ** Linear functions. **The student formulates equations and
inequalities based on linear functions,

uses a variety of methods to solve them, and analyzes the solutions in terms of
the situation.

(A) The student analyzes situations involving linear functions and formulates
linear equations or

inequalities to solve problems.

(B) The student investigates methods for solving linear equations and
inequalities using

[concrete] models, graphs, and the properties of equality, selects a method, and
solves the

equations and inequalities.

(C) For given contexts, the student interprets and determines the reasonableness
of solutions to

linear equations and inequalities.

A(c)(4) ** Linear functions. **The student
formulates systems of linear equations from problem situations,

uses a variety of methods to solve them, and analyzes the solutions in terms of
the situation.

(A) The student analyzes situations and formulates systems of linear equations
to solve

problems.

(B) The student solves systems of linear equations using [concrete] models,
graphs, tables, and

algebraic methods.

(C) For given contexts, the student interprets and determines the reasonableness
of solutions to

systems of linear equations.

**Objective 5:**

The student will demonstrate an understanding of quadratic and other nonlinear

functions.

A(d)(1)** Quadratic and other nonlinear functions. **The student understands
that the graphs of

quadratic functions are affected by the parameters of the function and can
interpret and describe

the effects of changes in the parameters of quadratic functions.

(B) The student investigates, describes, and predicts the effects of changes in
on the graph

of y = ax^{2}.

(C) The student investigates, describes, and predicts the effects of changes in
on the graph

of y = x^{2} + c.

(D) For problem situations, the student analyzes graphs of quadratic functions
and draws

conclusions.

A(d)(2) **Quadratic and other nonlinear functions. **The student understands
there is more than one

way to solve a quadratic equation and solves them using appropriate methods.

(A) The student solves quadratic equations using [concrete] models, tables,
graphs, and

algebraic methods.

(B) The student relates the solutions of quadratic equations to the roots of
their functions .

A(d)(3) **Quadratic and other nonlinear functions. **The student understands
there are situations

modeled by functions that are neither linear nor quadratic and models the
situations.

(A) The student uses [patterns to generate] the laws of exponents and applies
them in problemsolving

situations.