Symmetry in Functions

How can you determine if a function has line symmetry?

• Check if the function is unchanged when reflected over the y = x line.

• Check if the function is unchanged when reflected over the origin.

• Check if the function is unchanged when reflected over the x-axis.

• Check if the function is unchanged when reflected over the y-axis.

What is true about the graph?

• It is an even function. There is symmetry along the origin.

• It is an even. There is symmetry along the y-axis.

• It is an odd function. There is symmetry along the y-axis.

• It is an odd function. There is symmetry along the origin.

What do these functions have in common?

• Not enough information.

• They are all even functions. There is symmetry along the origin.

• They are all even. There is symmetry along the y-axis.

• They are all odd functions. There is symmetry along the y-axis.

• They are all odd functions. There is symmetry along the origin.

What do these functions have in common?

• Not enough information.

• They are all even functions. There is symmetry along the origin.

• They are all even. There is symmetry along the y-axis.

• They are all odd functions. There is symmetry along the y-axis.

• They are all odd functions. There is symmetry along the origin.

• absolute value

• rational

• exponential

What type of symmetry does the function have?

• none

• reflection symmetry

• rotation symmetry

Tell if the function is even, odd or neither and choose the correct explanation.

• Even, there is symmetry along the x-axis.

• Even, there is symmetry along the y-axis.

• Odd, there is symmetry along the x-axis.

• Odd, there is symmetry along the origin.

What type of symmetry does the function have?

• none

• reflection symmetry

• rotation symmetry

What is point symmetry in a function?

• Symmetry with respect to a point

• Symmetry with respect to an angle

• Symmetry with respect to a curve

• Symmetry with respect to a line

How can you determine if a function has point symmetry?

• Check if the function remains the same after rotation.

• Check if the function remains the same after reflection across the x-axis.

• Check if the function remains the same after translation.

• Check if the function remains the same after reflection across the y-axis.