AI Tutor
Imagine grabbing the graph of a curve by its peaks and valleys and pulling it upward like taffy, or flattening it toward the ground. In mathematics, that exact physical intuition is controlled by a single outside number.
To understand how this scaling works on every point of a graph, let's look at what happens to the output values.

Multiplying the Output

When we multiply a function by an outside constant to form g(x)=a⋅f(x)g(x) = a \cdot f(x), every original yy-value is multiplied by aa, while the input xx-value remains completely unchanged.
This means every coordinate point (x,y)(x, y) on the parent function shifts directly to the transformed coordinate (x,a⋅y)(x, a \cdot y).
How does the size of that multiplier determine whether the curve stretches taller or flattens out?

Stretches vs. Compressions

If ∣a∣>1|a| > 1, the function undergoes a vertical stretch by a factor of ∣a∣|a|, pulling all points farther away from the xx-axis.
If 0<∣a∣<10 < |a| < 1, the function undergoes a vertical compression (or vertical shrink) by a factor of ∣a∣|a|, pushing all points closer to the xx-axis.
What does this step-by-step mapping look like when we track key anchor points on a radical function?

Worked Example: Square Root Function