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 way:
1. Both graphs represent the floor function, where [x] denotes the greatest integer less than or equal to x. This means that for any given x-value, the corresponding y-value in both graphs will be the greatest integer less than or equal to x.
2. The graph of y = [x] is a step function, consisting of horizontal lines at each integer value on the x-axis. Each horizontal line represents a different integer value, and when x lies between two consecutive integers, y takes the value of the lower integer.
3. The graph of y = [x] - 15 is also a step function but vertically shifted downward by 15 units compared to the graph of y = [x]. This means that each horizontal line in the second graph is 15 units below the corresponding line in the first graph.
4. Both graphs have the same shape and pattern, except for the vertical shift. The distance between any two consecutive horizontal lines in the second graph will be the same as the distance between the corresponding lines in the first graph.
In summary, the graphs of y = [x] and y = [x] - 15 are similar in shape and pattern, with the latter graph shifted downward by 15 units. They both represent the floor function, where the y-values are the greatest integers less than or equal to the corresponding x-values.