Lian Joerss Post # 4

Hello class! My name is Lian and today we will be learning about symmetry. Symmetry is all around us- in nature, buildings, etc. Symmetry is when an image, shape, or line looks the same when it is flipped, rotated, or turned. The flipped shape is usually "mirrored" and is identical to the shape it is symmetrical with. 

The most common symmetry is vertical symmetry which looks like this:  

The shapes and images are split down the middle (vertically) and the both halves of the shapes are exactly alike -this is the line of symmetry. The line of symmetry is where a shape or image is divided so that the image is mirrored and "equal".  Other examples of lines of symmetry are this: 

 

As you can see, there can be various ways in which images are symmetrical. The shapes above also show horizontal, diagonal, and rotational types of symmetry. The square, for instance, has all of the different types of symmetry that allow the image to be reflected when divided along the line of symmetry.

Symmetry is important in math and can be applied to graphical functions to help us determine if the functions are odd or even. On a graph, the "lines of symmetry" are mainly either the x-axis, y-axis, or the origin. 

When a line (function) is symmetric about the y-axis AND f(x) and f(-x) are equal, then the function is even. 

When a line (function) is symmetric about the origin AND f(-x) and -f(x) are equal, then the function is odd. 

This is what odd and even functions look like: