5. Transformations of Linear and Absolute Value Functions
Sign In
Consider vertical translations, horizontal translations, and reflections.
y=f(x)+k is a translation k units up, y=f(x−h) is a translation h units right, and y=-f(x) is a reflection in the x-axis of the parent function f.
Let's compare the graphs of y=f(x)+k, y=f(x−h), and y=-f(x) to the graph of the parent function f by using a table.
| Transformations of f(x) | |
|---|---|
| Vertical Translations | Translation up k units, k>0y=f(x)+k
|
| Translation down k units, k>0y=f(x)−k
| |
| Horizontal Translations | Translation right h units, h>0y=f(x−h)
|
| Translation left h units, h>0y=f(x+h)
| |
| Reflection | In the x-axisy=-f(x)
|
| In the y-axisy=f(-x)
| |
Supposing that k and h are positive numbers, y=f(x)+k is a translation k units up, y=f(x−h) is a translation h units right, and y=-f(x) is a reflection in the x-axis of the parent function f.