Symmetry Tests

• y-axis symmetry

• x-axis symmetry

• origin symmetry

• None of these symmetries

• All 3 of these symmetries

• y-axis symmetry

• x-axis symmetry

• origin symmetry

• None of these symmetries

• All 3 of these symmetries

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the test for origin symmetry?

• (x,y) <-> (-x, -y)

• (x,y) <-> (-x, y)

• (x,y) <-> (x, -y)

• (x,y) <-> (y,x)

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the test for x-axis symmetry?

• (x,y) <-> (-x, -y)

• (x,y) <-> (-x, y)

• (x,y) <-> (x, -y)

• (x,y) <-> (y,x)

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the test for y=x symmetry?

• (x,y) <-> (-x, -y)

• (x,y) <-> (-x, y)

• (x,y) <-> (x, -y)

• (x,y) <-> (y,x)

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the test for y-axis symmetry?

• (x,y) <-> (-x, -y)

• (x,y) <-> (-x, y)

• (x,y) <-> (x, -y)

• (x,y) <-> (y,x)

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the symmetry test for an odd function?

• (x,y) <-> (-x, -y)

• (x,y) <-> (-x, y)

• (x,y) <-> ( -y, -x)

• (x,y) <-> (y,x)

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the symmetry test for an even function?

• (x,y) <-> (-x, -y)

• (x,y) <-> (-x, y)

• (x,y) <-> ( -y, -x)

• (x,y) <-> (y,x)

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the symmetry test for y = -x symmetry?

• (x,y) <-> (-x, -y)

• (x,y) <-> (-x, y)

• (x,y) <-> ( -y, -x)

• (x,y) <-> (y,x)

Identify the type of symmetry based on the graph:

• i only

• ii only

• iii only

• i, ii, and iii