Introduction to Rational Functions - Problem 4

The most basic graph of a rational function, y = 1/x , has two "branches" and two boundary lines, or asymptotes. Since x could never be zero in this function, we have a vertical line at x = 0 that the branches will never touch. Similarly, there is no way that the output y could equal zero, so we have a horizontal boundary line at y = 0. Here we look at shifting the branches vertically ( the horizontal asymptote will move up or down along with the branches) by adding or subtracting a constant after the fraction. We can also shift the graph horizontally by adding or subtracting a constant in the denominator with x. In this case, the vertical asymptote will shift as well. These vertical transformations apply to other function types, or families, as well.