A constant added to or subtracted from a function shifts its graph vertically. A constant added to or subtracted from a function's input shifts its graph horizontally.

Multiplying a function by a constant stretches or squishes the function vertically. Multiplying a function's input by a constant stretches or squishes the function horizontally.

Multiplying a function by a negative number causes its graph to reflect over the x-axis. Multiplying a function's input by a negative number causes its graph to reflect over the y-axis.

Taking the absolute value of a function moves all the points on its graph above the x-axis. Taking the absolute value of a function's input causes the left side of the graph to clone the right side.

Since I never miss a change to procrastinate, I decided to spend some time compiling a "cheat sheet" for function transformations.I've included the following 8 transformations: