1. Absolute Value Transformations
BY: JASMINE WOODS

2. Absolute Value We were use to seeing this back in Algebra 1: f(x) = x
Now in Algebra 11 we are using the absolute value:
f(x) = |x|
(parent function)

3. The Different Types of Transformations

4. Vertical Translation f(x) = |x| + d or f(x) = |x| - d
d, represents a number, this means the v
shaped line on your graph will move up a
certain number or down a certain number.
*vertical: located outside of |x|*

5. Horizontal Translation
f(x) = |x + d| or f(x) = |x - d|
d, also represents a number located inside
the bars, these numbers tell you if the v shaped line moves left (+) or right (-)
*horizontal: think opposite/ located inside |x|*

6. Vertical Stretch/ Compression
f(x)= b|x|
b, represents a number that could be more
than 1 (stretch) or less than 1 (compression).
Located outside the bars before the x.

7. Horizontal Stretch/Compression
f(x)= |bx|
b, represents a number that could be more
than 1 (compression) or less than 1 (stretch).
Located inside the bars in front of the x

8. Reflections
Reflection over the X axis f(x) = - |x|
Reflection over the Y axis f(x) = |-x|

9. Writing equations of the function, f(x)= |x|
The equation, f(x), has been reflected over the x- axis and has a vertical shift up three units.
It’s important to underline all the transformations going on so you can write out your equation.

10. F(x) = - |x| + 3

11. 2.) The equation, f(x), has been vertically stretched by a factor of four and horizontally shifted right two units.

12. F(x) = 4 |x-2|

13. 3.) The equation, f(x), has been horizontally stretched by a factor of three and reflected over the x- axis.

14. F(x) = - |1 / 3|