Question

If (3,-18) is on an odd function, what other point is guaranteed to be on the function?

a) (-3, 18)

b) (3, 18)

c) (-3, -18)

d) (18, 3)

Answer 1

The point (-3, 18) is guaranteed to be on the odd function if the point (3, -18) is included because odd functions satisfy the symmetry property y(x) = -y(-x).

Step-by-step explanation:

If (3,-18) is on an odd function, an odd function, by definition, satisfies the property that y(x) = −y(−x). This means that if a point (x, y) is on the function, then the point −(x, y) will also be on the function with its y-coordinate sign-flipped. For the point (3, -18), the corresponding point that must be on the function is (-3, 18). Therefore, the answer to the question is (-3, 18), which aligns with option (a).