Answered: Geometry Question

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Expert Solution

Step 1: Given,

The graph of a function. This graph is a transformation of the function $f (x) = | x | .$ We have to write the equation for the function graphed.

Step 2: Concept Used

The function transformation rules:

f (x) + b shifts the function b units upward.
f (x) – b shifts the function b units downward.
f (x + b) shifts the function b units to the left.
f (x – b) shifts the function b units to the right.
–f (x) reflects the function in the x-axis (that is, upside-down).
f (–x) reflects the function in the y-axis (that is, swapping the left and right sides).
y = Cf(x) then if C > 1 then stretches it in the y-direction and if 0 < C < 1 then compresses it
y = f(Cx) then if C > 1 then compresses it in the x-direction and if then 0 < C < 1 stretches it