Essential Question:  How do we determine whether a graph, equation, or data set represents a function and what type of function a graph, equation, or data set represents?

Unit Rationale:  Understanding and modeling with functions, building on students’ previous learning about linear and exponential relationships, helps us expand our understand of real-world situations using other non-linear models, setting the stage for deeper exploration in Algebra 2 and Pre-Calculus.

As a result of this unit, students will be able to:

Ø  Determine whether a relationship or set of data is a function; identify components such as domain, range, independent and dependent variables.

Ø  Model functions with multiple representations, including graphs, tables, words, and symbols (using function notation).

Ø  Identify, model and use specific types of functions such as absolute value and quadratic.

Vocabulary:

·        Functions

·        Vertical line test

·        Independent variable

·        Dependent variable

·        Domain

·        Range

·        Increasing

·        Decreasing

·        Linear

·        Nonlinear

·        Discrete graph

·        Continuous graph

·        Absolute value function

·        Squaring function

·        Parabola

·        Step function

·        Discontinuous

Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements. 

Focus Standards:

*A1.3.A  Determine whether a relationship is a functions and identify the domain, range, roots, and independent and dependent variables.

*A1.3.B  Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.

Supporting Standards:

*A1.2.B  Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions and evaluate algebraic expressions that involve variables.

*A1.3.C  Evaluate f(x) for a and solve for x in the equation f(x)=b

*A1.4.A  Write and solve linear equations and inequalities in one variable

A1.5.A  Represent a quadratic function with a symbolic expression, as a graph in a table, and with a description and make connections among the representations.

Reasoning, Problem Solving, and Communication Standards:

A1.8.E  Read and interpret diagrams, graphs, and text containing the symbols, language and conventions of mathematics.