Even Odd Neither Functions

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 is a neither function?

Back

A function is called 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

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

Back

Neither. f(-x) = x^4 - x^3, which is not equal to f(x) or -f(x).

Front

Determine if g(x) = x^4 + x^2 is even, odd, or neither.

Back

Even. g(-x) = x^4 + x^2, which is equal to g(x).

Front

Determine if h(x) = x^5 + x^3 is even, odd, or neither.

Back

Odd. h(-x) = -x^5 - x^3, which is equal to -h(x).

Front

Determine if k(x) = x^3 + x is even, odd, or neither.

Back

Odd. k(-x) = -x^3 - x, which is equal to -k(x).

Front

What is the graphical representation of an even function?

Back

The graph of an even function is symmetric about the y-axis.

Front

What is the graphical representation of an odd function?

Back

The graph of an odd function is symmetric about the origin.

Front

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

Back

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