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1.1 FUNCTIONS

1.1 FUNCTIONS. Relation: An identified relationship between two variables that may be expressed as ordered pairs, a table of values, a graph or an equation. Ex 1. (6,216), (7, 343) , (8, 512).

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1.1 FUNCTIONS

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  1. 1.1 FUNCTIONS Relation: An identified relationship between two variables that may be expressed as ordered pairs, a table of values, a graph or an equation Ex 1. (6,216), (7, 343) , (8, 512) Function: A set of ordered pairs in which, for every value of x, there is only one value of y. Yes, it’s a function Ex 2. (1, 5), (2, 6) , (3, 7) , (4, 8) No, it’s not a function Ex 3. (2, 7), (3, 8), (3, 9), (4, 9)

  2. Vertical Line Test If a line passes through more than one point on a graph of a relation, then the relation is not a function. Yes, it’s a function No, it’s not a function

  3. -3 -2 -1 0 1 2 3 Domain & Range Domain = The set of the first elements in a relation (think of the x-values)

  4. 3 2 1 0 -1 -2 Domain & Range Range = The set of the second elements in a relation (think of the y-values)

  5. Domain & Range Ex 1: State the Domain & Range of each. Determine if it is a function a) (-2, 2), (-3, 3), (-4, 4) , (-3, 5) , (-1, 6) Domain = { } -4, -3, -2, -1 Range = { } 2, 3, 4, 5, 6 No, it’s not a function… The value of –3 in the domain has two different values in the range.

  6. Domain & Range Ex 2: State the Domain & Range of each. Determine if it is a function b) y = x2 Yes, it’s a function We say “ x such that x is an element of the set of Real Numbers” Domain = {x | x  } Range = { y | y  0 , y  }

  7. x y -2 -1 0 1 Domain & Range Ex 3: State the Domain & Range of each. Determine if it is a function b) y = -2x + 3 Domain = {x | x  } Yes, it’s a function Range = {y | y  }

  8. Function Notation “y depends on x” is a function of x x – y notationfunction notation y = 2x + 3 f(x) = 2x + 3 We say, “f of x” or “f at x” Therefore, y = f(x) Ex. Sub in x = 2 into y = 6x – 3 OR f(x) = 6x - 3 y = 6(2) – 3 f(2) = 6(2) – 3 Look at the examples in your text = 12 - 3 = 12 – 3 = 9 = 9

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