Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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Concept explainers

Transformation of Graphs
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Question

If f is an even function, determine whether g is even, odd, or neither. Explain.
(a)
g(x) = −f(x)
even
odd
neither

Explain.
The graph is a reflection in the x-axis.
The graph is a reflection in the y-axis.
The graph is a vertical translation of f.
The graph is a horizontal translation of f.
The graph is symmetric about the origin.

(b)
g(x) = f(−x)
even
odd
neither

Explain.
The graph is a reflection in the x-axis.
The graph is a reflection in the y-axis.
The graph is a vertical translation of f.
The graph is a horizontal translation of f.
The graph is symmetric about the origin.

(c)
g(x) = f(x) − 3
even
odd
neither

Explain.
The graph is a reflection in the x-axis.
The graph is a reflection in the y-axis.
The graph is a vertical translation of f.
The graph is a horizontal translation of f.
The graph is symmetric about the origin.

(d)
g(x) = f(x − 3)
even
odd
neither

Explain.
The graph is a reflection in the x-axis.
The graph is a reflection in the y-axis.
The graph is a vertical translation of f.
The graph is a horizontal translation of f.
The graph is symmetric about the origin.

r ris an even tunction, determine whether g is even,oda, or neither. Explain. (a) gx) x) O even odd O neither Explain. O The graph is a reflection in the x-axis. O The graph is a reflection in the y-axis. O The graph is a vertical translation of f O The graph is a horizontal translation of f O The graph is symmetric about the origin. (b) g(x)-x) O even O odd O neither Explain. O The graph is a reflection in thexaxis. O The graph is a reflection in the y-axis. O The graph is a vertical translation of f O The graph is a horizontal translation of f O The graph is symmetric about the origin. (c) gx)x- 3 O even odd O neither Explain. O The graph is a reflection in the x-axis. O The graph is a reflection in the y-axis. O The graph is a vertical translation of f O The graph is a horizontal translation of f O The graph is symmetric about the origin. (d) gx)-x 3) O even odd O neither Explain. O The graph is a reflection in thexaxis. O The graph is a reflection in the y-axis. O The graph is a vertical translation of f O The graph is a horizontal translation of f O The graph is symmetric about the origin. Need Help? Read ItTalk to a Tuter
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Transcribed Image Text:r ris an even tunction, determine whether g is even,oda, or neither. Explain. (a) gx) x) O even odd O neither Explain. O The graph is a reflection in the x-axis. O The graph is a reflection in the y-axis. O The graph is a vertical translation of f O The graph is a horizontal translation of f O The graph is symmetric about the origin. (b) g(x)-x) O even O odd O neither Explain. O The graph is a reflection in thexaxis. O The graph is a reflection in the y-axis. O The graph is a vertical translation of f O The graph is a horizontal translation of f O The graph is symmetric about the origin. (c) gx)x- 3 O even odd O neither Explain. O The graph is a reflection in the x-axis. O The graph is a reflection in the y-axis. O The graph is a vertical translation of f O The graph is a horizontal translation of f O The graph is symmetric about the origin. (d) gx)-x 3) O even odd O neither Explain. O The graph is a reflection in thexaxis. O The graph is a reflection in the y-axis. O The graph is a vertical translation of f O The graph is a horizontal translation of f O The graph is symmetric about the origin. Need Help? Read ItTalk to a Tuter
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