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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

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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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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Step 1

Given: f(x) is an even function. Hence by definition, f(-x) = f(x). We will use this result in all the subparts of the question solved below.

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