Even, Odd or Neither

Front

What is an even function?

Back

A function f(x) is called an even function if for every x in the domain, f(-x) = f(x). This means the graph of the function is symmetric with respect to the y-axis.

Front

What is an odd function?

Back

A function f(x) is called an odd function if for every x in the domain, f(-x) = -f(x). This means the graph of the function is symmetric with respect to the origin.

Front

What does it mean if a function is neither even nor odd?

Back

A function is neither even nor odd if it does not satisfy the conditions for being even or odd. Its graph does not exhibit symmetry with respect to the y-axis or the origin.

Front

Example of an even function: f(x) = x^2. Is it even, odd, or neither?

Back

Even. Since f(-x) = (-x)^2 = x^2 = f(x).

Front

Example of an odd function: f(x) = x^3. Is it even, odd, or neither?

Back

Odd. Since f(-x) = (-x)^3 = -x^3 = -f(x).

Front

Determine if f(x) = 2x^4 - 3 is even, odd, or neither.

Back

Even. Since f(-x) = 2(-x)^4 - 3 = 2x^4 - 3 = f(x).

Front

Determine if f(x) = x^3 - x is even, odd, or neither.

Back

Odd. Since f(-x) = (-x)^3 - (-x) = -x^3 + x = -f(x).

Front

What is the symmetry of even functions?

Back

Even functions are symmetric about the y-axis.

Front

What is the symmetry of odd functions?

Back

Odd functions are symmetric about the origin.

Front

If f(x) = x^2 + 1, is it even, odd, or neither?

Back

Even. Since f(-x) = (-x)^2 + 1 = x^2 + 1 = f(x).