Answered: Graph the function g(x) by transforming…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 31E

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Question

Graph the function g(x) by transforming the graph of a basic function, f(x).

g(x)= 3/((5x-15)^2)-6 (Use (-1,1) and (1,1) as the two points in the 1st graph. (Graph 0.)

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Step 1: Basic information

$L e t g i v e n f u n c t i o n b e f (x) I f i t t r a n s f o r m e d b y + a u n i t i n x - d i r e c t i o n, t h e n t r a n s f o r m e d f u n c t i o n, s a y g (x) i s : g (x) = f (x - a) N o t e : F r o m g i v e n e x p r e s s i o n o f g (x), i t i s u n c l e a r w h e t h e r' - 6' i s a t d e n o m i n a t o r o r n u m e r a t o r . S o, b o t h e x p r e s s i o n h a s b e e n s o l v e d . g (x) = \frac{3}{{(5 x - 15)}^{2}} - 6, a n d g (x) = \frac{3}{{(5 x - 15)}^{2} - 6}$

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