The transformation from f(x) = |x| to v(x) = -3 |x + 1| + 4 involves a vertical reflection, a horizontal shift left by 1 unit, and a vertical shift up by 4 units.
The transformation from the graph of f(x) = |x| to v(x) = -3 |x + 1| + 4 involves three key changes:
1. Reflection:
- The negative sign in front of 3 reflects the graph vertically, causing it to flip upside down.
2. Horizontal Shift:
- The expression |x + 1| shifts the graph horizontally by 1 unit to the left.
3. Vertical Shift:
- The constant +4 shifts the entire graph vertically upward by 4 units.
These transformations collectively result in an inverted, horizontally shifted, and vertically shifted version of the original absolute value function.