Relations & Functions

Define, evaluate, and compare functions * Build new functions from existing functions * Analyze functions using different representations * Use functions to model relationships between quantities * Represent and solve equations and inequalities graphically * Understand the concept of a function and use function notation * Interpret functions that arise in applications in terms of the context

Topics

Relations vs. Functions
Domain and Range
Discrete vs. Continuous
Real World Graphs
Equations as Functions: Graphing by a Function Table
Function Notation: Evaluating Functions
Zeros and Functions

Prerequisites

Evalauating expressions
Using tables, graphs and equations
Graphing the coordinate plane
Solving two-step equations
Solving absolute value equations

Goals

Identify functions (equations, graphs, tables, maps)
Understand that the graph of "f" is the graph of the equation y=f(x)
Understand that when "x" is an element of the input of a function, f(x) represents the corresponding output
Use function notation to evaluate functions (linear, quadratic, polynomial, exponential, absolute value)
Use function notation to evaluate functions Ex: f(x+1)
Evaluate and simplify using basic function notation Ex: 2f(3)-4f(5)
Graph a function by creating a table of points
Write basic function rules using a table of values
Identify characteristics of functions (domain and range) in all forms (table, function, and graph)
Use technology to graph functions and identify key features (domain, range)
Identify function families (linear, exponential, absolute value)
Understand how changing the parameters of a function will cause the graph to shift up, down, right or left
Identify patterns in sequences and represent arithmetic sequences in explicit form