Question

The graph of the function y = f(x) is symmetrical about the line x = 2, then ______.

Options

• f(x) = –f(–x)

• f(2 + x) = f(2 – x)

• f(x) = f(–x)

• f(x + 2) = f(x – 2)

Answer 1

The graph of the function y = f(x) is symmetrical about the line x = 2, then f(2 + x) = f(2 – x).

Explanation:

If a function h(x) is symmetrical about the y-axis (i.e. x = 0), then we can write h(x) = h(−x)

It can also be written as h(0 + x) = h(0 − x)

∴ A function f(x) which is symmetrical about x = 2, can be written as f(2 + x) = f(2 − x)