Aim What are the even and odd functions

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Aim: What are the even and odd functions? Do Now: Use your graphing calculator

Aim: What are the even and odd functions? Do Now: Use your graphing calculator to graph each of the following functions. Draw a sketch of the graph under its equation.

All four functions are called EVEN functions. a) What type of symmetry does each

All four functions are called EVEN functions. a) What type of symmetry does each graph have? b) What is special about the exponents of each term in the functions? c) What happens when you evaluate f(x) for each of the functions?

Use your graphing calculator to graph each of the following functions. Draw a sketch

Use your graphing calculator to graph each of the following functions. Draw a sketch of the graph under its equation.

All of the above functions are called ODD functions. a) What type of symmetry

All of the above functions are called ODD functions. a) What type of symmetry does each graph have? b) What is special about the exponents of each term in the functions? c) What happens when you evaluate f(-x) for each of the functions?

Even functions • A graph has symmetry with respect to the y-axis if, whenever

Even functions • A graph has symmetry with respect to the y-axis if, whenever (x, y) is on the graph, so is the point ( -x, y). A function whose graph is symmetric with respect to the y-axis is an even function. Odd functions A graph has symmetry with respect to the origin if, whenever (x, y) is on the graph, so is the point (-x, -y). A function whose graph is symmetric with respect to the origin is an odd function. Test for even and odd functions A function f is even if, for each x in the domain of f, f(-x) = f(x). A function f is odd if, for each x in the domain of f, f(-x) = -f(x).

Algebraically, determine whether each function is odd, even or neither

Algebraically, determine whether each function is odd, even or neither

Each of the graphs below shows a portion of a graph of an even

Each of the graphs below shows a portion of a graph of an even function over the interval [-5, 5]. Complete these graphs.

Each of the graphs below shows a portion of a graph of an odd

Each of the graphs below shows a portion of a graph of an odd function over the interval [-5, 5]. Complete these graphs.

Table A shows a portion of a table of an even function and table

Table A shows a portion of a table of an even function and table B shows a portion of a table of an odd function. Complete these tables.