What type of symmetry does the graph of y = x3 exhibit?
Rotational symmetry of 90 degrees clockwise about the origin
Rotational symmetry of 180 degrees clockwise about the origin
Reflectional symmetry about the y-axis
Reflectional symmetry about the x-axis
The graph of the equation y = x^3 exhibits reflectional symmetry about the y-axis.
To determine the type of symmetry exhibited by the graph of y = x^3, let's break it down.
Rotational symmetry involves rotating the graph around an axis of rotation and having it look the same in different positions. However, the graph of y = x^3 does not have rotational symmetry because it does not retain its shape after any rotation.
Reflectional symmetry, on the other hand, involves reflecting the graph across an axis and having it remain the same. To determine if y = x^3 has reflectional symmetry about the y-axis, we can check if replacing x with -x in the equation (y = (-x)^3) gives us an equivalent equation to the original. Simplifying, we get y = -x^3. Since this equation is not equivalent to the original, y = x^3 does not have reflectional symmetry about the y-axis.
To check for reflectional symmetry about the x-axis, we can replace y with -y in the equation (y = x^3) and simplify. This results in -y = x^3. By multiplying both sides by -1, we get y = -x^3, which is equivalent to the original equation. Therefore, the graph of y = x^3 does exhibit reflectional symmetry about the x-axis.
In summary, the correct answer is: Reflectional symmetry about the x-axis.