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pre-calc sect. 1.6

# pre-calc sect. 1.6 - Section 1.6 Transformations Graphs of...

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Section 1.6 Transformations Graphs of Common Functions - Some graphs you should be able to recognize as we will use them a lot - See graphs in Table 1.6 on p.205 1.) Constant Function : c x f = ) ( 2.) Identity Function : x x f = ) ( 3.) Standard Quadratic Function : 2 ) ( x x f = 4.) Standard Cubic Function : 3 ) ( x x f = 5.) Square Root Function : x x f = ) ( 6.) Absolute Value Function : x x f = ) ( 7.) Standard Cubic Function : 3 ) ( x x f = --starting with basic graphs such as these, we can “transform” them into many other graphs Order of Transformations 1.) Horizontal Shifting 2.) Vertical/Horizontal Stretching or Shrinking 3.) Reflecting 4.) Vertical Shifting **Note : Very helpful table on p.213 to remind of different transformations Horizontal Shifts Let f be a function and c a positive real number. - The graph of y = f(x+c) is the graph of y = f(x) shifted to the left c units. - The graph of y = f(x-c) is the graph of y = f(x) shifted to the right c units. EX 1: Use the graph of f(x) = x 2 to obtain the graph of a) f(x) = (x – 2) 2 b) f(x) = (x + 1) 2

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Vertical Stretching or Shrinking
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pre-calc sect. 1.6 - Section 1.6 Transformations Graphs of...

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