Exploring Even and Odd Functions

What is the line of symmetry for an even function?

• Origin

• y = x

• y-axis

• x-axis

Which of the following is a characteristic of an even function?

• Symmetry with the y-axis

• Symmetry with the x-axis

• No symmetry

• Symmetry with the origin

How can you test if a function is odd?

• Reflect the graph over the y-axis

• Plug in both negative x and negative y and check if the equation stays the same

• Plug in negative y and check if the equation stays the same

• Plug in negative x and check if the equation stays the same

What is a unique property of odd functions?

• They have no symmetry

• They have symmetry with the origin

• They have symmetry with the y-axis

• They do not pass through the origin

What is the test for symmetry with the x-axis?

• Plug in negative x for x

• Plug in negative y for y

• Switch x and y

• Reflect the graph over the y-axis

Which of the following functions has symmetry with the line y = x?

• y = sin(x)

• y = 1/x

• y = x^3

• y = x^2

If a function is even and you are given a point (x, y), what is another point on the graph?

• (-x, -y)

• (-x, y)

• (x, -y)

• (y, x)

If a function is odd and you are given a point (x, y), what is another point on the graph?

• (-x, -y)

• (x, -y)

• (y, x)

• (-x, y)

What happens to a graph when you take the absolute value of the function?

• It reflects over the y-axis

• It reflects over the x-axis

• All negative y-values become positive

• All positive y-values become negative

What is the result of replacing x with -x in a function?

• Reflection over the x-axis

• Reflection over the y-axis

• No change

• Reflection over the origin