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.
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.
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
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
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
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.
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
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) - 3 = a2 - a - a + 1 - 3 = a2 - 2a - 2
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