What transformation could we do to the graph of that would result in the same graph? Examining the shape of the graph, we can see a symmetry between points to the left of the -axis and the points to the right of the -axis. Looking at the points on the graph where and , these opposite inputs have the same outputs since and . This means that if we reflect the graph across the -axis, it will look no different. This type of symmetry means is an even function.

What transformation could we do to the graph of that would result in the same graph? Examining the shape of the graph, we can see that there is a symmetry between points on opposite sides of the axes. Looking at the points on the graph where and , these opposite inputs have opposite outputs since and . So a transformation that takes the graph of to itself has to reflect across the -axis and the -axis. This type of symmetry is what makes an odd function.