SWBAT: −Match functions to their parent graphs −Find domain and range of functions from a graph −Determine if a function is even or odd −Give the domain and range of functions in various notations Parent Graphs, Domain, and Range

Domain  All the possible input values (x values) of a function.  Generally the domain of functions is all real numbers.  When is it not?  You will learn about a few more this year.  All the possible input values (x values) of a function.  Generally the domain of functions is all real numbers.  When is it not?  You will learn about a few more this year.

Range  All the possible output values (y values) of a function.  Each function has it’s own range, and often the best way to determine a range is to look at a graph.  Look at each y-value and see if the graph hits that value at all. If it never does (and never will) then that value is not in the range.  What functions do you know that have limited ranges?  All the possible output values (y values) of a function.  Each function has it’s own range, and often the best way to determine a range is to look at a graph.  Look at each y-value and see if the graph hits that value at all. If it never does (and never will) then that value is not in the range.  What functions do you know that have limited ranges?

Notation for Domain and Range  Three different notations : Set Notation, Algebraic Notation, and Interval Notation  Set Notation is usually for discrete data (individual points)  Algebraic Notation and Interval Notation are used for continuous data  Three different notations : Set Notation, Algebraic Notation, and Interval Notation  Set Notation is usually for discrete data (individual points)  Algebraic Notation and Interval Notation are used for continuous data

Set Notation  This table shows us a set of discrete data. We only know about the points given to us.  We need to use Set Notation and list the individual values in the domain and in the range.  Set notation uses brackets (the squiggly ones { } ) with the numbers listed in ascending order and are separated by commas.

Algebraic Notation vs. Interval Notation : Mostly a matter of preference Algebraic Notation Interval Notation

Piecewise Domain: Range: Even/Odd?: Domain: Range: Even/Odd?:

Constant Function Domain: Range: Even/Odd?:

Linear Function Domain: Range: Even/Odd?: Domain: Range: Even/Odd?:

Absolute Value Domain: Range: Even/Odd?:

Quadratic Domain: Range: Even/Odd?:

Square Root Domain: Range: Even/Odd?:

Cubic Domain: Range: Even/Odd?:

Cube Root Domain: Range: Even/Odd?: Domain: Range: Even/Odd?:

Rational Domain: Range: Even/Odd?: Domain: Range: Even/Odd?:

Rational Domain: Range: Even/Odd?: Domain: Range: Even/Odd?:

Logarithmic Domain: Range: Even/Odd?: Domain: Range: Even/Odd?:

Exponential Domain: Range: Even/Odd?: Domain: Range: Even/Odd?:

2.2 Polynomial Functions of Higher Degree SWBAT: −Identify the degree and leading coefficient of polynomials −Determine the end behavior of a polynomial from it’s equation −Find the real zeros of a polynomial from a graph, a table, and by factoring −Sketch a graph of a polynomial from a function SWBAT: −Identify the degree and leading coefficient of polynomials −Determine the end behavior of a polynomial from it’s equation −Find the real zeros of a polynomial from a graph, a table, and by factoring −Sketch a graph of a polynomial from a function

Polynomial Functions

If n is odd The Leading Coefficient Test: If n is odd If a is positive If a is negative

If n is even The Leading Coefficient Test: If n is even If a is positive If a is negative

Apply the Leading Coefficient Test to determine the end behavior

Zeros of a Polynomial Function

Real Zeros of Polynomial Functions

Find the zeros of each function

Repeated Zeros

Writing a Polynomial Function from the zeros Given the zeros 3, 3, -4, write a polynomial function.

Intermediate Value Theorem

Approximating the Zeros

Sketching the graph of a polynomial 1)Apply the Leading Coefficient Test to determine end behavior 2)Find the zeros 3)Find additional points 4)Draw the graph 1)Apply the Leading Coefficient Test to determine end behavior 2)Find the zeros 3)Find additional points 4)Draw the graph

Sketch the graph