Question

Write the equations for the basic absolute value equation y=|x-h|+k under the given transformations:

1. shift 1 unit to the right and up 2 units

2. shift 3 units to the left and 7 units down

3. vertical shrink by a factor of 1/3

4. vertical stretch by a factor of 3

Answer 1

Left & Right affect the h,
Up & Down affect the k,
Shrink & Stretch affect the "a" (which is in front of the absolute value expression).

1. shift 1 unit to the right and up 2 units → y = |x-1| + 2
2. shift 3 units to the left and 7 units down → y = |x + 7| - 7
3. vertical shrink by a factor of 1/3 → y =
`(1)/(3)`|x|
4. vertical stretch by a factor of 3 → y = 3 |x|