Symmetry with Odd and Even Functions

Front

What is an even function?

Back

A function f(x) is called an even function if for every x in the domain, f(-x) = f(x). This means the graph of the function is symmetric with respect to the y-axis.

Front

What is an odd function?

Back

A function f(x) is called an odd function if for every x in the domain, f(-x) = -f(x). This means the graph of the function is symmetric with respect to the origin.

Front

Do all even functions have symmetry to the x-axis?

Back

False. Even functions have symmetry with respect to the y-axis, not the x-axis.

Front

If a function is even and the point (3, 5) is on the graph, which other point must be on the graph?

Back

(−3, 5). For even functions, if (a, b) is on the graph, then (−a, b) must also be on the graph.

Front

If a function is odd and the point (2, 3) is on the graph, which other point must be on the graph?

Back

(−2, −3). For odd functions, if (a, b) is on the graph, then (−a, −b) must also be on the graph.

Front

What is the symmetry of the graph of an even function?

Back

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

Front

What is the symmetry of the graph of an odd function?

Back

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

Front

If a function has symmetry with respect to the x-axis, what can be said about the points on the graph?

Back

If (a, b) is on the graph, then (a, -b) must also be on the graph.

Front

Is the function f(x) = x^2 an even function?

Back

Yes, because f(-x) = (-x)^2 = x^2 = f(x).

Front

Is the function f(x) = x^3 an odd function?

Back

Yes, because f(-x) = (-x)^3 = -x^3 = -f(x).