Stretching and compression are important ways to change the shape of the graphs of functions.

Stretching

• Vertical Stretch: When you multiply a function by a number bigger than 1, it makes it taller. For example, if you take the function $f(x) = x^2$ and change it to $g(x) = 3x^2$, the graph stretches upwards by a factor of 3.

• Horizontal Stretch: To stretch a graph sideways, you multiply the input by a fraction that is less than 1. This means changing $f(x) = x^2$ to $g(x) = (0.5x)^2$. This stretches the graph sideways by 2.

Compression

• Vertical Compression: If you multiply by a number between 0 and 1, the graph gets shorter. For example, changing $f(x) = x^2$ to $g(x) = 0.5x^2$ squishes the graph down.

• Horizontal Compression: To make the graph squish together sideways, you multiply the input by a number bigger than 1. Changing $f(x) = x^2$ to $g(x) = (2x)^2$ shrinks the graph sideways by half.

These changes help us see how the shape of the graph changes while keeping the x-values the same.