a) Use the asymptotes and intercepts to make a quick sketch of the function f(x) =x-2/x+4 and its reciprocal,g(x)= x+4/x-2 , on the same set of axes.
b) Describe the symmetry in the graphs in part a).
c) Determine the equation of the mirror line in your graph from part a).
d) Determine intervals of increase and decrease for both f and g. How do the sets of intervals compare?
e) Does the pattern from part d) occur for all pairs of functions f(x) =x+b/x+d and , g(x) =x+d/x+b, b≠d ? Explain why or why not.
I know a few
a) Here are both graphs : https://www.desmos.com/calculator/lzspxc52ys
b) and c).....the line of symmetry is x = -1 ( I believe this is also the mirror line )
d) (x + 4) /(x -2) has no interval of increase ...it decreases on (-inf, -2) and (-2, inf)
Conversely ( -2) /(x + 4) has no interval of decrease ....it increases on ( -inf, -4) and (-4 , inf)
e) Sorry.....I do not know the answer to this one......