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AlgebraQ&A Libraryr 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 TuterQuestion

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

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.

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