Introduction to Rational Functions - Problem 5

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. We can reflect both branches of the graph across the x-axis by putting a negative in front of the fraction. This would make all of the outputs, or y-values, change their positive/negative sign, which "flips" the graph upside down. If there are other transformations to be applied as well, we'll do the reflection first, and then any horizontal or vertical shifts.