You saw in Lesson 9.7 that a transformation of the parent function f (x) = 1/x is a rotated hyperbola. Are there other kinds of rational functions that are also rotated hyperbolas? Recall that any conic section can be written in the general quadratic form, Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.
a. Rewrite the equation y = x + 1 + 1/x -1 in general quadratic form, if possible. Is the graph actually a rotated hyperbola?
b. Look back at your graph of y = x - / x2 -4 from Exercise 7. Does the graph appear to be a rotated hyperbola?
c. Rewrite the equation y = x - 3/x2 - 4 in general quadratic form, if possible. Is the graph actually a rotated hyperbola?
d. Write a conjecture that describes how you can tell, based on an equation, what rational functions are rotated hyperbolas.