Final answer:
The transformation y = 1/2*|x + 2| - 1 consists of shifting the graph left by 2 units, compressing it vertically by a factor of 1/2, and then moving it down by 1 unit, creating a V-shaped graph with a vertex at (-2, -1).
Step-by-step explanation:
The transformation described by the equation y = ½§|x + 2| - 1 includes several steps. These transformations can be broken down as follows:
- Addition of 2 inside the absolute value function shifts the graph horizontally to the left by 2 units.
- The multiplication by ½ outside the absolute value function compresses the graph vertically, reducing its steepness by half.
- Subtraction of 1 from the entire expression translates the graph downwards by 1 unit.
This results in a piecewise linear graph that is symmetrical about the y-axis but is not entirely symmetrical since a horizontal translation has occurred.
It begins at a vertex located at (-2, -1) and proceeds outward with a slope of ½ in the positive direction and -½ in the negative direction of the x-axis.