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Section 1.2

Section 1.2. function domain & range family of functions symmetry even function vs odd functions. Definitions. Function For each input (called x), there is exactly one output for f(x) How do you determine if a graph, equation, or set of data represents a function? Domain

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Section 1.2

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

  2. Definitions • Function • For each input (called x), there is exactly one output for f(x) • How do you determine if a graph, equation, or set of data represents a function? • Domain • Every input that is valid for a function creates a set called the domain • Range • When you evaluate all the inputs, the corresponding outputs create a set called the range.

  3. Family of Functions • Identity Function: • Domain • Range

  4. Family of Functions • Quadratic function: • Domain • Range

  5. Family of Functions • Cubic function: • Domain • Range

  6. Family of Functions • Absolute Value function: • Domain • Range

  7. Family of Functions • Square Root function: • Domain • Range

  8. Family of Functions • Cubed Root function: • Domain • Range

  9. Family of Functions • Rational function: • Domain • Range

  10. Family of Functions • Rational (squared) function: • Domain • Range

  11. Example: Find the domain and range.You should know the shape of the graph without your calculator. • a) • c) • e) • g) • b) • d) • f)

  12. Symmetry • If 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.

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

  14. Symmetry • If 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).

  15. Symmetric wrt the x-axis Testing for Symmetry wrt the x-axis • Plug in –y for y into your equation. • The graph of an equation is symmetric wrt the x-axis if an equivalent equation results. • Example 2: Test the equation below for symmetry wrt the x-axis.

  16. Symmetry • If 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.

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

  18. Example 4: Determine the symmetry of the graph of each equation. If a graph is symmetric wrt the y-axis and x-axis, then it is symmetric wrt the origin. y-axis x-axis origin y-axis origin x-axis

  19. Example 4: Determine whether each function is even, odd, or neither. odd function even function not a function

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