Describe how the graph shown below is related to the graph of
y=|x|
The graph shown below is the graph of y = |x| + 2.
Here's how it is related to the graph of y=|x|:
1. Shifted Upward: The graph of y = |x| + 2 is obtained by taking the graph of y = |x| and shifting it upward by 2 units. This means that every point on the graph of y = |x| + 2 is 2 units higher than the corresponding point on the graph of y = |x|.
2. Same Shape: The overall shape of the graph remains the same. It is still a V-shape with the vertex at the origin. The arms of the V extend upwards and downwards at the same steepness, forming a symmetrical graph.
3. Intersection Points: The graph of y = |x| + 2 intersects the x-axis at the same points as the graph of y = |x|. The points of intersection are (0, 2) and (-0, -2). This is because the absolute value of any real number is equal to 0 when the number itself is 0. So, when x = 0, both y = |x| and y = |x| + 2 will have the same value of 2.
Overall, the graph of y = |x| + 2 is simply a vertically shifted version of the graph of y = |x|. It has the same shape and intersects the x-axis at two points, but it is higher up by 2 units.