Even function

Definition

An even function is a type of function where $f(x) = f(-x)$ for all $x$ in its domain. Graphically, this means the function is symmetric with respect to the y-axis.

5 Must Know Facts For Your Next Test

1. An even function satisfies the property $f(x) = f(-x)$.
2. The graph of an even function is symmetric about the y-axis.
3. Examples of even functions include $f(x) = x^2$ and $f(x) = \cos(x)$.
4. If a function is not symmetric about the y-axis, it is not an even function.
5. In trigonometry, verifying if a trigonometric identity involves an even function can simplify problem-solving.

Review Questions

• What property must an even function satisfy?
• How can you visually identify an even function on its graph?
• Give two examples of common even functions in algebra and trigonometry.

Related terms

Odd Function: A type of function where $f(-x) = -f(x)$ for all $x$ in its domain, indicating symmetry about the origin.

Symmetry: A characteristic of graphs where one half is a mirror image of the other half. For even functions, this symmetry is about the y-axis.

Trigonometric Identity: A mathematical equation involving trigonometric functions that holds true for all values within its domain.