Answered: how using transformations can help one…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

how using transformations can help one graph functions?

Expert Solution

Step 1: Basic information

$f (x) = k n o w n p a r e n t f u n c t i o n, l i k e \sin (x), \cos (x), . . ., e x p (x), \ln (x), . e t c g (x) = t r a n s f o r m e d f u n c t i o n S a y, g (x) = c f (b (x - a)) + d$

$A f f e c t s o f c o n s \tan t s a, b, c, d o n f (x) . a = \{\begin{cases} S h i f t t h e f (x) r i g h t w a r d s b y' a' s t e p s i f a > 0 \\ S h i f t t h e f (x) l e f t t w a r d s b y' a' s t e p s i f a < 0 \end{cases} b = \{\begin{cases} s t r e t c h t h e f (x - a) h o r i z o n t a l l y b y f a c t o r' b' i f 0 < |b| < 1 \\ c o m p r e s s t h e f (x - a) h o r i z o n t a l l y b y f a c t o r' b' i f |b| > 1 \\ G i v e s m i r r o r i m a g e o f' f (|b| (x - a))' a c r o s s y = b, i f b < 0 . \end{cases} c = \{\begin{cases} c o m p r e s s t h e' f (b (x - a))' v e r t i c a l l y b y f a c t o r' c' i f 0 < |c| < 1 \\ s t r e t c h t h e' f (b (x - a))' v e r t i c a l l y b y f a c t o r' c' i f |c| > 1 \\ G i v e s m i r r o r i m a g e o f' |c| f (b (x - a))' a c r o s s x = c, i f c < 0 . \end{cases} d = \{\begin{cases} S h i f t t h e' c f (b (x - a)) u p w a r d s b y' d' s t e p s i f d > 0 \\ S h i f t t h e' c f (b (x - a)) d o w n w a r d s b y' d' s t e p s i f d < 0 \end{cases}$