Question

Which of the following statements is/are true about an odd function f(x)?

• A. f(-x) = f(x)
• B. f(-x) = - f(x)
• C. Its graph is symmetric about the origin
• D. Its graph is symmetric about the x-axis
• E. Its graph is symmetric about the y-axis

Answer 1

Answer: (B), (C)

Its graph is symmetric about the origin

A function is said to be an odd function when f(-x) = - f(x). If the value of f(1) is y, the value of f(-1) should be -y. When we plot the graph for any odd function, its graph is symmetrical about the opposite quadrants or we can also say it is symmetrical about the origin.

For example

f(x) = x

f(-x) = -x

Here, when we replace x with (-x) we get,

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

This condition is necessary for any function to be an odd function.