How to know when there is a vertical dilation or a horizontal dilation?

Question

asked Mar 21, 2019 111k views

1 Answer

Fishinear · Answer 1 · 2019-03-25T19:02:56+0000

Given a function
f(x) and a number
$k\\eq 0$ , if you multiply the whole function by
, you have a vertical dilation:

$f(x) \to kf(x) = \begin{cases} \text{vertical dilation} & \text{ if }k>1\\\text{vertical compression} & \text{ if }0<k<1 \end{cases}$

If
k<0 , 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
, you have a horizontal dilation:

$f(x) \to f(kx) = \begin{cases} \text{horizontal dilation} & \text{ if }0<k<1\\\text{horizontal compression} & \text{ if }k>1 \end{cases}$

If
k<0 , you follow the same steps as before, but you also reflect the function around the y-axis.