For the function f whose graph is given, state the following?

heres the graph: http://www.webassign.net/scalcet7/2-6-003.gif

I must find out what the vertical and horizontal asympotes are

AND
what the limit is as f(x) approaches 1 and approaches 3

Question

For the function f whose graph is given, state the following?

heres the graph: http://www.webassign.net/scalcet7/2-6-003.gif

I must find out what the vertical and horizontal asympotes are

AND
what the limit is as f(x) approaches 1  and approaches 3

tkhunny · Answer

#1 - From a drawing, you cannot KNOW anything unless it is VERY CLEARLY labeled.

Vertical Asymptotes

x = 1 (unbounded positive) and x = 3 (unbounded negative) seem clear enough.

Horizontal Asymptotes, not so much.

Is it y = 2 in the negative x-direction and y = -2 in the positive x-direction or are those not asymptotes at all?  Can't really say.  It is the nature of the drawing rather than a specific algebraic definition.

x-intercepts

I might buy (0,0), but the other two are not clear at all.  (-3.1,0) and (2.4,0)?  Somewhere around there.

Two other interesting points are local humps or troughs, around (-1.5,-1.2) and (4.5,-0.7).  Those might be fun to find more exactly.

There are also three more interesting points (points of inflection), but that may be a discussion for another day.

askme12345 · Answer

I input 1,3 and -2,2 as the horizontal and vertical asymptotes and the answer was marked incorrect. :(

tkhunny · Answer

Well, those are just numbers.  The vertical asymptotes are x = 1 and x = 3.  Those are equations of lines.

I already spoke to the ambiguity of the horizontal asymptotes.  I am not particularly confident that there are any.  Presumably, if they exist, they might be y = 2 and y = -2.