Enlargement of $y=f(x)$

For the function $y=f(ax)$.

1. If $a>1$, the graph of $y=f(x)$ contracts to $a$ times of the original along the $x$-axis. The $y$ intercept remains unchanged.
2. If $0<a<1$, the graph of $y=f(x)$ enlarges to ${\displaystyle \frac{1}{a}}$ times of the original along the $x$-axis. The $y$ intercept remains unchanged.

For the function $y=af(x)$.

1. If $a>1$, the graph of $y=f(x)$ enlarges to $a$ times of the original along the $y$-axis. The $x$ intercept(s) remain(s) unchanged.
2. If $0<a<1$, the graph of $y=f(x)$ contracts to ${\displaystyle \frac{1}{a}}$ times of the original along the $y$-axis. The $x$ intercept(s) remain(s) unchanged.

Same Topic:

Cosine Law Exterior Angle of Triangle Reflections of $y=f(x)$ Trigonometric Ratios of Special Angles