Exploring Even and Odd Functions

What type of symmetry does an even function exhibit?

• Reflective symmetry over the x-axis

• No symmetry

• Rotational symmetry

• Reflective symmetry over the y-axis

In an even function, if a point (x, y) exists on the graph, what is the corresponding point?

• (-x, y)

• (x, y)

• (x, -y)

• (-x, -y)

What is the algebraic condition for a function to be even?

• f(x) = -f(x)

• f(x) = f(-x)

• f(-x) = f(x)

• f(-x) = -f(x)

What type of symmetry does an odd function exhibit?

• Reflective symmetry over the y-axis

• Reflective symmetry over the x-axis

• No symmetry

• Rotational symmetry around the origin

In an odd function, if a point (x, y) exists on the graph, what is the corresponding point?

• (x, y)

• (-x, -y)

• (x, -y)

• (-x, y)

What is the algebraic condition for a function to be odd?

• f(-x) = f(x)

• f(-x) = -f(x)

• f(x) = f(-x)

• f(x) = -f(x)

What happens to the graph of a function with x-axis symmetry?

• It is not a function

• It has rotational symmetry

• It is a function

• It has reflective symmetry over the y-axis

In x-axis symmetry, if a point (x, y) exists on the graph, what is the corresponding point?

• (-x, -y)

• (x, -y)

• (-x, y)

• (x, y)

Why does x-axis symmetry not have a special name?

• Because it has rotational symmetry

• Because it has reflective symmetry over the y-axis

• Because it is not a function

• Because it is a function

What is the result when substituting -y for y in a function with x-axis symmetry?

• The result is undefined

• The result is the negative of the original function

• The result is the same as the original function

• The result is different from the original function