Transformation Notation

$y = a f (k (x - p)) + q$
where:
vertical stretch factor of $| a |$
if $a$ < 0, reflection in x-axis
horizontal stretch factor of $\frac{1}{| k |}$
if k < 0, reflection in y-axis
horizontal shift by $p$
vertical shift by $q$

Related transformations are transformations to a graph which produce the same graph

Example

for $f (x) = \sqrt{x}$ , a vertical stretch factor of 2 is equal to horizontal stretch factor of $\frac{1}{4}$

y=2\sqrt

```desmos-graph

y=\sqrt

Explanation:
$$

\begin{align}
y & =2\sqrt{ x } \
& =\sqrt{ 2^{2} }\sqrt{ x } \
& =\sqrt{ 4x }
\end

Transformation Notation

Related Transformations