| \({\text{Transformations of Absolute Value Functions}}\) |
| \(\underline{\text{Function/Transformation}}\) |
\(\underline{\text{Description}}\) |
| \(|x|\) |
\(\text{Parent Function}\) |
| \(|x+h|\) |
\(\text{Translated } h \text{ units left}\) |
| \(|x-h|\) |
\(\text{Translated } h \text{ units right}\) |
| \(|x|+k\) |
\(\text{Translated } k \text{ units up}\) |
| \(|x|-k\) |
\(\text{Translated } k \text{ units down}\) |
| \(a \cdot |x|\) |
\(\text{Vertical dilation (stretch) by a factor of } a \) |
| \(\frac{1}{a} \cdot |x|\) |
\(\text{Vertical dilation (shrink) by a factor of } \frac{1}{a}\) |
| \(|b \cdot x|\) |
\(\text{horizontal dilation (shrink) by a factor of } \frac{1}{b} \) |
| \(\left|\frac{1}{b} \cdot x\right|\) |
\(\text{horizontal dilation (stretch) by a factor of }b \) |
| \(-|x|\) |
\(\text{Reflection over x-axis}\) |
| \(|-x|\) |
\(\text{Reflection over y-axis}\) |
