When we stretch graphs up and down or side to side, we see some pretty big changes in their shapes. Let's break down what this means!

Vertical Stretches

• What It Is: A vertical stretch happens when we make the output of a function bigger by a number greater than 1.
• Example: If we have the function $f(x) = x^2$ and we stretch it vertically by 2, we get a new function: $g(x) = 2f(x) = 2x^2$. This makes the graph look "taller" and steeper.
• Picture It: The original graph is a "U" shape that goes up, but the stretched version goes up much faster.

Horizontal Stretches

• What It Is: A horizontal stretch happens when we make the input of a function smaller by a number between 0 and 1.
• Example: Using the same function, if we stretch it horizontally by 0.5, we get $h(x) = f(2x) = (2x)^2 = 4x^2$. This makes the graph look "wider."
• Picture It: The new graph still looks like a "U," but it opens up more gently, giving it a wider curve.

Knowing how these stretches work helps us understand how graphs will look when we change them!