Even, Odd or Neither

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). Graphically, even functions are symmetric about 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). Graphically, odd functions are symmetric about 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 about the y-axis or the origin.

Front

Identify if the function f(x) = x^2 is even, odd, or neither.

Back

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

Front

Identify if the function f(x) = x^3 is even, odd, or neither.

Back

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

Front

Identify if the function f(x) = x^4 + x^2 is even, odd, or neither.

Back

Even (since f(-x) = (-x)^4 + (-x)^2 = x^4 + x^2 = f(x)).

Front

Identify if the function f(x) = x^5 + x^3 is even, odd, or neither.

Back

Odd (since f(-x) = (-x)^5 + (-x)^3 = -x^5 - x^3 = -f(x)).

Front

What is the graphical representation of an even function?

Back

The graph of an even function is symmetric with respect to the y-axis.

Front

What is the graphical representation of an odd function?

Back

The graph of an odd function is symmetric with respect to the origin.

Front

Provide an example of an even function.

Back

f(x) = x^2 is an example of an even function.