Example 3 for the following function identify the

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Example 3 For the following function, identify the parent function, write the equation in standard transformation form, then identify the values of A, B, C, and D. 1 ( ) 3 2 4 2 h x x ³ ± . Example 4 Write the equations of the functions if the same transformations applied above are applied to the following parent functions (a) 2 ( ) f x x (b) 1 ( ) f x x (c) ( ) ln f x x (d) ( ) x f x e A function ( ) g x is said to be written in Standard Transformation form if it is written as ( ) ( ( )) g x Af B x c D ± ³ Where ( ) f x is the parent function or original function. 4 25 IEE 3 g x _AfCBCx d TD parent y r A L Bit h x ztT4xI t3 C D 3 A Yz 13 4 C Yz D 3 fC z 4 x I Yt3 Txt 21 t3 THINK 3gC AfCBC d TD 464 DG zte 1 3
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As you work through more and more examples, the shift transformations will become very intuitive. Dilations, however, can be tricky to interpret and tricky to graph, especially since several algebra texts do a poor job of describing what these transformations actually do. I will teach you what I expect you to do. NOTES: We always interpret a dilation as a stretch (if it gets bigger) or a compression (if it gets smaller). We can abbreviate “by a factor of” as “bfo.” When we say “bfo,” the number that follows MUST BE GREATER THAN ONE!! A is the vertical dilation factor If |A| ! 1, ____________________________________________________________________ If 0 <|A|< 1, __________________________________________________________________ If A ² 0, _____________________________________________________________________ |B| is the horizontal dilation factor If |B| ! 1, ____________________________________________________________________ If 0 <|B|< 1 , __________________________________________________________________ If B ² 0 , _____________________________________________________________________ C is the horizontal shift constant If C ! 0 ,_____________________________________________________________________ If C ² 0 ,_____________________________________________________________________ D is the vertical shift constant
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