2-1: Functions & Their GraphsObjectives:1. I will determine if a function is linear.2. I will find the given value of the ...
Graphs of a FunctionVertical Line Test:    If a vertical line is passed over the graph and it intersects the graph in exac...
Does the graph represent a function?Name the domain and range.                   Yes          x        D: all reals       ...
Does the graph represent a function?Name the domain and range.                   No           x       D: x ≥ 1/2          ...
Does the graph represent a function?Name the domain and range.                   Yes            x      D: all reals       ...
Function Notation• When we know that a relation is a  function, the “y” in the equation can  be replaced with f(x).• f(x) ...
Value of a FunctionSince the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2.Find f(4): f(4...
Value of a FunctionIf g(s) = 2s + 3, find g(-2).     g(-2) = 2(-2) + 3           =-4 + 3           = -1     g(-2) = -1
Value of a FunctionIf h(x) = x2 - x + 7, find h(2c).  h(2c) = (2c)2 – (2c) + 7        = 4c2 - 2c + 7
Value of a FunctionIf f(k) = k2 - 3, find f(a - 1)     f(a - 1)=(a - 1)2 - 3    (Remember FOIL?!)            =(a-1)(a-1) -...
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2.1 a relations and functions

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2.1 a relations and functions

  1. 1. 2-1: Functions & Their GraphsObjectives:1. I will determine if a function is linear.2. I will find the given value of the function.3. I will graph linear functions.
  2. 2. Graphs of a FunctionVertical Line Test: If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function.
  3. 3. Does the graph represent a function?Name the domain and range. Yes x D: all reals R: all reals y Yes x D: all reals R: y ≥ -6 y
  4. 4. Does the graph represent a function?Name the domain and range. No x D: x ≥ 1/2 R: all reals y No x D: all reals R: all reals y
  5. 5. Does the graph represent a function?Name the domain and range. Yes x D: all reals R: y ≥ -6 y No x D: x = 2 R: all reals y
  6. 6. Function Notation• When we know that a relation is a function, the “y” in the equation can be replaced with f(x).• f(x) is simply a notation to designate a function. It is pronounced ‘f’ of ‘x’.• The ‘f’ names the function, the ‘x’ tells the variable that is being used.
  7. 7. Value of a FunctionSince the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2.Find f(4): f(4) = 4 - 2 f(4) = 2
  8. 8. Value of a FunctionIf g(s) = 2s + 3, find g(-2). g(-2) = 2(-2) + 3 =-4 + 3 = -1 g(-2) = -1
  9. 9. Value of a FunctionIf h(x) = x2 - x + 7, find h(2c). h(2c) = (2c)2 – (2c) + 7 = 4c2 - 2c + 7
  10. 10. Value of a FunctionIf f(k) = k2 - 3, find f(a - 1) f(a - 1)=(a - 1)2 - 3 (Remember FOIL?!) =(a-1)(a-1) - 3 = a2 - a - a + 1 - 3 = a2 - 2a - 2

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