5/1 PreCal - 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

If a function has symmetry with respect to the origin and the point (-3, 5) is on the graph, which other point must be on the graph?

Back

(3, -5)

Front

Identify the type of symmetry: If a function is symmetric with respect to the y-axis, what can be said about its graph?

Back

The graph is unchanged when reflected across the y-axis.

Front

If a function is an even function and the point (-2, 7) is on the graph, which other point must be on the graph?

Back

(2, 7)

Front

Back

y-axis symmetry.

Front

Back

Origin symmetry.

Front

What is the definition of symmetry with respect to the x-axis?

Back

A function is symmetric with respect to the x-axis if for every point (x, y) on the graph, the point (x, -y) is also on the graph.

Front

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

Back

If the graph of the function is symmetric with respect to the origin, then the function is odd.

Front

What is the relationship between the points on the graph of an even function?

Back

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