## The vertical asymptotes of this graph is x=1 because the graph gets closer and closer to the line x = 1 but never touches the line x = 1. the values of the constants and coefficients of this graph are a = 2, b = 1, c = 1, and d = -1.

In assignment 1, we showed that in general, given a rational function where f(x) = ax + b and g(x) = cx + d, the horizontal asymptotes occur where the domain of the function breaks, that is where the denominator g(x) is equal to zero. In this case cx + d = 0, thus the vertical asymptote is x = -d/c. The horizontal asymptotes occur where y = a/c because as x gets infinitely large or small then the numerator tends to something extremely large times a or something extremely small times a, while the denominator tends to something extremely large times c or something extremely small times c.

In the case of the hyperbola given in the example, we see that the asymptotes are y = 2, a horizontal line, and x = 1, a vertical line. Because the asymptotes consist of a horizontal line and a vertical line, then the lines are perpendicular. A hyperbola which has asymptotes meeting at right angles is called a rectangular hyperbola. In the above example the center of the hyperbola is at (1,2). In general the center of a rectangular hyperbola is at (-d/c, a/c).

## 6) The y-intercepts occur at the point (0, b/d)

7) The hyperbola f0rmed is a rectangular hyperbola.