Even Odd or Neither Functions

Front

What is an even function?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain of f. The graph of an even function is symmetric about the y-axis.

Front

What is an odd function?

Back

A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f. The graph of an odd function is 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

How can you determine if a function is even?

Back

To determine if a function is even, check if f(-x) = f(x) for all x in the domain. If true, the function is even.

Front

How can you determine if a function is odd?

Back

To determine if a function is odd, check if f(-x) = -f(x) for all x in the domain. If true, the function is odd.

Front

What is the graph of f(x) = x^2? Is it even, odd, or neither?

Back

The graph of f(x) = x^2 is an even function because f(-x) = f(x). It is symmetric about the y-axis.

Front

What is the graph of f(x) = x^3? Is it even, odd, or neither?

Back

The graph of f(x) = x^3 is an odd function because f(-x) = -f(x). It is symmetric about the origin.

Front

What is the graph of f(x) = x^4 + x^2? Is it even, odd, or neither?

Back

The graph of f(x) = x^4 + x^2 is an even function because f(-x) = f(x). It is symmetric about the y-axis.

Front

What is the graph of f(x) = x^5 + x^3? Is it even, odd, or neither?

Back

The graph of f(x) = x^5 + x^3 is an odd function because f(-x) = -f(x). It is symmetric about the origin.

Front

What is a relative maximum?

Back

A relative maximum is a point on the graph of a function where the function value is higher than the values of the function at nearby points.