Stretching and Contracting Graphs

When we multiply a function by a constant c, the graph of the new function created is not longer the identical shape. Instead, one of two things happens:

If the constant c has an absolute value greater than 1, then the graph of this new function $LaTeX: c\cdot f\left(x\right)$ $c\cdot f\left(x\right)$ will be made by stretching the graph of the function $LaTeX: y=f\left(x\right)\:$ $y=f\left(x\right)\:$ vertically by a factor of c. This makes the graph appear narrower.
If the constant c has an absolute value that is between 0 and 1, then the graph of $LaTeX: c\cdot f\left(x\right)$ $c\cdot f\left(x\right)$ will be made by compressing the graph of $LaTeX: y=f\left(x\right)\:$ $y=f\left(x\right)\:$ , making the graph wider rather than narrower.

Here is a video demonstrating this: