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

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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.

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Family of Functions zIdentity Function: yDomain yRange

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Family of Functions zQuadratic function: yDomain yRange

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Family of Functions zCubic function: yDomain yRange

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Family of Functions zAbsolute Value function: yDomain yRange

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Family of Functions zSquare Root function: yDomain yRange

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Family of Functions zCubed Root function: yDomain yRange

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Family of Functions zRational function: yDomain yRange

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Family of Functions zRational (squared) function: yDomain yRange

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

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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.

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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

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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).

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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

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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.

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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

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

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

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Functions and Graphs 1.2. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

Functions and Graphs 1.2. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

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