Given a function [tex] f(x) [/tex] and a number [tex] k\neq 0 [/tex], if you multiply the whole function by [tex] k [/tex], you have a vertical dilation:
[tex] f(x) \to kf(x) = \begin{cases} \text{vertical dilation} & \text{ if }k>1\\\text{vertical compression} & \text{ if }0<k<1 \end{cases} [/tex]
If [tex] k<0[/tex], you follow the same steps as before, but you also reflect the function around the x-axis.
If, instead, you multiply only the argument by [tex] k [/tex], you have a horizontal dilation:
[tex] f(x) \to f(kx) = \begin{cases} \text{horizontal dilation} & \text{ if }0<k<1\\\text{horizontal compression} & \text{ if }k>1 \end{cases} [/tex]
If [tex] k<0[/tex], you follow the same steps as before, but you also reflect the function around the y-axis.
