Question

If f(x) is an odd function, which statement about the graph f(x) must be true?

Answer 1

Answer:

The correct answer is A)  It has rotational symmetry about the origin.

Step-by-step explanation:

In principle, the graph of an odd function is symmetric with respect to the origin. This simply means that the point (0 ,0) acts as a mirror line to the function so that one half of the function looks exactly like the other half when reflected over the origin.

A function f(x) is said to be odd if and only if;

f(-x) = -f(x)

The ultimate example of an odd function is the sine function. Consider the function below;

f(x) = sin(x)

Then;

f(-x) = sin(-x) = -sin(x) = -f(x)

Working with actual values;

sin(-30) = -sin(30) = -0.5

A graph of the function f(x) = sin(x) is shown in the attachment below;

If the graph is rotated about the origin, we would still end up with the same graph.

In summary, an odd function is symmetric with respect to the origin and has rotational symmetry about the origin.