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4.8 Functions and Relations

4.8 Functions and Relations. Goal: Decide whether a relation is a function and use function notation. Definitions. Relation - Any set of ordered pairs. Function -A type of relation where there is exactly one output for every input . For every x there is exactly one y. x. y. y.

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4.8 Functions and Relations

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  1. 4.8 Functions and Relations Goal: Decide whether a relation is a function and use function notation

  2. Definitions Relation - Any set of ordered pairs Function -A type of relation where there is exactly one output for every input. For every x there is exactly one y.

  3. x y y x 1 6 1 6 2 7 2 7 Not a Function Function

  4. y = 2x x-y chart mapping x y input output -2 -1 0 1 2 -4 -2 0 2 4 -4 -2 -2 -1 0 0 1 2 2 4 Function

  5. Determine whether the equation is a function. output output input input x y x y 2 1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 2 1 0 1 2 -2 0 0 -2 -1 -1 1 1 0 0 1 1 2 2 2 2 Function Not a Function

  6. Vertical Line Test - Functions y y y y x x x x Function y y y y x x x x

  7. Vertical Line Test - Functions y y y y x x x x Function Function y y y y x x x x

  8. Vertical Line Test - Functions y y y y x x x x Function Function Not a Function y y y y x x x x

  9. Vertical Line Test - Functions y y y y x x x x Function Function Function Not a Function y y y y x x x x

  10. Vertical Line Test - Functions y y y y x x x x Function Function Function Not a Function y y y y x x x x Not a Function Not a Function Not a Function Function

  11. Tell whether the relation below is a function. output input 1) 3) y 0 1 x 5 Function Not a Function 2 3 x y output input 2) 4) -3 -3 -3 -3 -1 0 1 2 3 -2 4 -1 Not a Function 5 Not a Function 0 6

  12. Function Notation

  13. Evaluate the following.

  14. Evaluate the function over the domain, x = -1, x = 0, x = 2.

  15. Graph the linear function. f(x) x -3 -2 -1 0 1 2 3 6 5 4 3 2 1 0 x

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