Q1.3 Even/Odd Functions

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. This means that f(-x) is not equal to f(x) or -f(x) for all x.

Front

Provide an example of an even function.

Back

f(x) = x² is an even function because f(-x) = (-x)² = x².

Front

Provide an example of an odd function.

Back

f(x) = x³ is an odd function because f(-x) = (-x)³ = -x³.

Front

What is the graphical representation of an even function?

Back

Even functions are symmetric with respect to the y-axis.

Front

What is the graphical representation of an odd function?

Back

Odd functions are symmetric with respect to the origin.

Front

How can you determine if a function is even or odd using its graph?

Back

To determine if a function is even, check for y-axis symmetry. To determine if it is odd, check for origin symmetry.

Front

What is the significance of the degree of a polynomial in determining if it is even or odd?

Back

Even-degree polynomials can be even functions, while odd-degree polynomials can be odd functions. The coefficients of the terms also affect this.

Front

If f(x) = 2x⁴ - 3x² + 1, is it even, odd, or neither?

Back

f(x) is even because f(-x) = 2(-x)⁴ - 3(-x)² + 1 = 2x⁴ - 3x² + 1 = f(x).