even and odd functions algebraically

Front

What is an even function?

Back

A function f(x) is called even 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 odd 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

Back

Even function.

Front

Back

Odd function.

Front

What is the definition of a function being neither even nor odd?

Back

A function is neither even nor odd if it does not satisfy the conditions for being even or odd for all x in its domain.

Front

Identify the function that is odd: f(x) = 3x^4 - 4x^3, g(x) = 5x^4 + 3x^2, h(x) = 6x^5 - x^3, k(x) = x^6 + 8x^2.

Back

h(x) = 6x^5 - x^3.

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^3, is it even, odd, or neither?

Back

Odd function.

Front

If f(x) = x^2 + 3x + 9, is it even, odd, or neither?

Back

Neither even nor odd.