how are the functions y=× and y=×-3 related? How are their graphs related?
The functions y=x and y=x-3 are related because y=x-3 is formed by shifting the graph of y=x downward by 3 units.
The graph of y=x is a straight line that passes through the origin (0,0) in a 45-degree angle. The graph of y=x-3 is also a straight line, but it is shifted downward by 3 units.
In terms of graph transformations, the graph of y=x is the parent function and the graph of y=x-3 can be obtained by translating the parent function downward.
The functions y = x and y = x - 3 are related because they both represent linear functions. The second function, y = x - 3, is obtained by subtracting 3 from the first function, y = x.
To understand how their graphs are related, let's examine their slope and y-intercept. The first function, y = x, has a slope of 1 and a y-intercept of 0, meaning it passes through the origin (0, 0). The second function, y = x - 3, also has a slope of 1, but its y-intercept is -3, so it intersects the y-axis at the point (0, -3).
In terms of their graphs, both functions will appear as straight lines on a coordinate plane. However, the graph of y = x - 3 will be shifted downward by 3 units compared to the graph of y = x. In other words, the graph of y = x - 3 will be lower than the graph of y = x at every point.
In summary, the functions y = x and y = x - 3 are related because one is derived from the other by subtracting a constant. Their graphs are related by a vertical shift downward of 3 units for the second function.