Describe how the graphs of Y=|x| and y=|x+2| are related.
The graphs of y = |x| and y = |x + 2| are related through a vertical shift. The graph of y = |x| is the standard absolute value function, symmetric about the y-axis and passing through the origin. It consists of two V-shaped halves, one in the positive x-axis region and the other in the negative x-axis region.
When we add 2 to the x-coordinate of each point on the graph of y = |x|, we shift the entire graph 2 units to the left. Thus, the graph of y = |x + 2| is obtained by horizontally sliding the graph of y = |x| to the left by 2 units.
Both graphs still have the same V-shape, but the vertex of the left half of the graph of y = |x + 2| will be at (-2, 0) instead of (0, 0). The right half of the graph of y = |x + 2| occupies the positive x-axis region, while the left half occupies the negative x-axis region.
In summary, the graph of y = |x + 2| is a horizontally shifted version of the graph of y = |x|, shifting two units to the left.