What effect does the addition of 'd' in the expression f(x) + d have on the graph?

When adding 'd' to the expression f(x), resulting in f(x) + d, this affects the graph of the function by performing a vertical shift. Specifically, the entire graph will move up by 'd' units if d is positive, and it will move down by 'd' units if d is negative.

This means that any point on the original graph of f(x) will increase its y-coordinate by 'd' for every corresponding x-coordinate after the transformation. So if you had a point (x, f(x)), after adding 'd', this point would be moved to (x, f(x) + d). This addition does not affect the x-coordinates of the points on the graph, hence no horizontal shift occurs, and it also does not involve any stretching, compression, or reflection of the graph. The primary transformation is a straightforward upward or downward shift, emphasizing how such vertical translations simply adjust the height of the graph in the coordinate plane.