How do the graphs of y = start fraction 1 over x end fraction and y = Start Fraction 3 over x End Fraction – 4 compare?
The graphs of y = 1/x and y = 3/x - 4 are both rational functions that have a hyperbolic shape.
- The graph of y = 1/x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. As x approaches infinity or negative infinity, y approaches 0. The graph is in the first and third quadrants only.
- The graph of y = 3/x - 4 has a vertical asymptote at x = 0 and a horizontal asymptote at y = -4. As x approaches infinity or negative infinity, y approaches -4. The graph is also in the first and third quadrants only.
In comparison, the graph of y = 3/x - 4 is similar to the graph of y = 1/x, but it is vertically shifted down by 4 units compared to the graph of y = 1/x. The horizontal asymptote of y = 3/x - 4 is also shifted down by 4 units compared to the horizontal asymptote of y = 1/x.