Question

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16. Determine if the functions represent even, odd, or neither.

Answer 1

a) even

b) neither

c) odd

Explanation:

A function is "even" when there is symmetry about the y-axis.

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

• f(x, y) = f(-x, y)

A function is "odd" when there is origin symmetry.

Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:

• f(x, y) = f(-x, -y)

Graph a

From inspection of the graph, the curve appears to be symmetrical about the y-axis. Therefore, the function is even.

Graph b

This is an absolute value function. It has no symmetry about the y-axis or the origin. Therefore, the function is neither.

Graph c

From inspection of the graph, the curve appears to be symmetric with respect to the origin. Therefore, the function is odd.