Q1.3 Even/Odd Functions

Front

What is an even function?

Back

A function f(x) is called even if f(-x) = f(x) for all x in the domain of f. Graphically, even functions are symmetric about the y-axis.

Front

What is an odd function?

Back

A function f(x) is called odd if f(-x) = -f(x) for all x in the domain of f. 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. This means that f(-x) is not equal to f(x) or -f(x).

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^3 - x^2 is even, odd, or neither.

Back

Neither (since f(-x) = -x^3 - x^2, which is not equal to f(x) or -f(x)).

Front

Which of the following functions is even? f(x) = x^4 + x^3, g(x) = x^4 + x^2, h(x) = x^5 + x^3, k(x) = x^3 + x

Back

g(x) = x^4 + x^2 (since f(-x) = g(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

If f(x) = x^4 + 2x^2 + 1, is it even, odd, or neither?

Back

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