89.1k views
5 votes
Describe the transformation y=1/2*|x+2|-1

User Jordashiro
by
8.1k points

1 Answer

4 votes

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.

User Cicakman
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories