Describe how the graphs of y =|x| and y =|x|-15 are related
The graphs of y = |x| and y = |x| - 15 are related in the following ways:
1. Parallel Shift: The graph of y = |x| - 15 is obtained by shifting the graph of y = |x| downward by 15 units. This means that every point on the graph of y = |x| - 15 is 15 units below the corresponding point on the graph of y = |x|.
2. Intersection with y-axis: The graph of y = |x| intersects the y-axis at the point (0, 0), representing the absolute value of x when x is 0. On the other hand, the graph of y = |x| - 15 intersects the y-axis at the point (0, -15), representing the absolute value of x minus 15 when x is 0.
3. Symmetry: Both graphs are symmetric about the y-axis. This means that if a point (x, y) lies on the graph, the point (-x, y) will also lie on the graph. For example, if (2, 2) lies on the graph of y = |x|, then (-2, 2) will also lie on the graph. The same symmetry applies to the graph of y = |x| - 15.
4. Shape: The shape of both graphs is V-shaped, with the vertex at the origin (0, 0). However, the graph of y = |x| - 15 is shifted downward compared to the graph of y = |x|.
In summary, the graph of y = |x| - 15 is similar to the graph of y = |x|, but it is shifted downward by 15 units and intersects the y-axis at a different point.
The graphs of y = |x| and y = |x| - 15 are related through a vertical shift.
The graph of y = |x| represents the absolute value function, which can be defined as y = x if x is positive or zero, and y = -x if x is negative.
The second equation, y = |x| - 15, is obtained by subtracting 15 from the y-values of the absolute value function. This results in a downward shift of the graph by 15 units.
To visualize the relationship, consider the point (0, 0) on the graph of y = |x|. This point represents the vertex of the graph, where the absolute value of x is zero. On the graph of y = |x| - 15, this same point would be shifted downward by 15 units, resulting in the point (0, -15).
Similarly, if you pick any other point on the graph of y = |x| and subtract 15 from its y-coordinate, you will obtain the corresponding point on the graph of y = |x| - 15, but shifted downward by 15 units.
In summary, the graphs of y = |x| and y = |x| - 15 are related because the latter is obtained by shifting the former downward by 15 units.
To understand how the graphs of y = |x| and y = |x| - 15 are related, let's first define the absolute value function. The absolute value of a number is its distance from zero on the number line. Therefore, the absolute value function |x| takes any real number x and returns its positive value.
The graph of y = |x| is a V-shape, also known as a "V-shaped absolute value graph." It opens upwards and the vertex of the graph is at the origin (0, 0). The primary characteristic of this graph is that it is symmetrical with respect to the y-axis.
Now let's examine y = |x| - 15. To understand how it relates to the previous graph, we need to note that subtracting a constant value, in this case 15, will essentially shift the entire graph downward by 15 units. This 15-unit shift downward will affect all the points on the graph.
The graph of y = |x| - 15 will still maintain the same V-shape, but the entire graph will shift downward by 15 units. The vertex, which was at the origin (0, 0) in the previous graph, will now be at (0, -15). All the other points on the graph will similarly shift downward by 15 units.
In summary, the graphs of y = |x| and y = |x| - 15 are related in that they both have V-shaped absolute value graphs, but the second graph is shifted down 15 units compared to the first graph.