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.

Tags

CCSS.HSF.BF.B.3

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.

Tags

CCSS.HSF.BF.B.3

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).

Tags

CCSS.HSF.BF.B.3

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)).

Tags

CCSS.HSF.BF.B.3

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)).

Tags

CCSS.HSF.BF.B.3

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)).

Tags

CCSS.HSF.BF.B.3

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)).

Tags

CCSS.HSF.BF.B.3

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.

Tags

CCSS.HSF.BF.B.3

Front

What is the graphical representation of an odd function?

Back

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

Tags

CCSS.HSF.BF.B.3

Front

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

Back

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

Tags

CCSS.HSF.BF.B.3