use the asymptotes and intercepts to make a quick sketch of the function f(x)= x-2 (numerator) x+4(denominator) and its reciprocal f^r = x+4 (numerator) x-2 (denominator) on the same set of axes.

Question

b) describe the symmetry in the graphs in part a)
c) determine the intervals of increase and decrease for both f and f^r, how do the sets of intervals compare?
d) would the pattern occur for all pairs of functions f(x)= x+b (numerator) x+d and f^r(x) = x+d (numerator)and x+b (denominator)? explain why or why not?

Answer 1

so we have
f(x) = (x-2)/(x+4)
and
g(x) = (x+4)/(x-2)

Using one of my favourite websites:
Wolfram
http://www.wolframalpha.com/input/?i=plot+%28x-2%29%2F%28x%2B4%29%3B%28x%2B4%29%2F%28x-2%29

You should be able to answer your questions from the graph of the two functions