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Describe the transformation y=1/2*|x+2|-1

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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.

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User Cicakman
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