# Section 1.2 o function o domain & range o family of functions o symmetry o even function vs odd functions.

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Section 1.2 o function o domain & range o family of functions o symmetry o even function vs odd functions

Definitions zFunction yFor each input (called x), there is exactly one output for f(x) yHow do you determine if a graph, equation, or set of data represents a function? zDomain yEvery input that is valid for a function creates a set called the domain zRange yWhen you evaluate all the inputs, the corresponding outputs create a set called the range.

Family of Functions zIdentity Function: yDomain yRange

Family of Functions zQuadratic function: yDomain yRange

Family of Functions zCubic function: yDomain yRange

Family of Functions zAbsolute Value function: yDomain yRange

Family of Functions zSquare Root function: yDomain yRange

Family of Functions zCubed Root function: yDomain yRange

Family of Functions zRational function: yDomain yRange

Family of Functions zRational (squared) function: yDomain yRange

Example: Find the domain and range. You should know the shape of the graph without your calculator. za) zc) ze) zg) zb) zd) zf)

Symmetry zIf the graph of an equation is symmetric wrt the y-axis and contains the point (x,y), then the graph also contains the point (-x,y). These functions are called even functions.

Testing for Symmetry wrt the y-axis z Plug in –x for x into your equation. z The graph of an equation is symmetric wrt the y-axis if an equivalent equation results. z Example 1: Test the equation below for symmetry wrt the y-axis. Symmetric wrt the y-axis

Symmetry zIf the graph of an equation is symmetric wrt the x-axis and contains the point (x,y), then the graph also contains the point (x,-y).

Testing for Symmetry wrt the x-axis zPzPlug in –y for y into your equation. zTzThe graph of an equation is symmetric wrt the x-axis if an equivalent equation results. zEzExample 2: Test the equation below for symmetry wrt the x-axis. Symmetric wrt the x-axis

Symmetry zIf the graph of an equation is symmetric wrt the origin and contains the point (x,y), then the graph also contains the point (-x,-y). These functions are called odd functions.

Testing for Symmetry wrt the origin z Plug in –x for x and –y for y into the eqn. z The graph of an equation is symmetric wrt the origin if an equivalent equation results. z Example 3: Test the equation below for symmetry wrt the origin. Symmetric wrt the origin

Example 4: Determine the symmetry of the graph of each equation.

Example 4: Determine whether each function is even, odd, or neither.

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