Question

F(x)= x g(x)=x+1 graph f/g

Answer 1

Answer:

Step-by-step explanation:

                   x

(f/g)(x) = -----------

                x + 1

Notice that x cannot be -1, which would lead to division by zero.  Thus, x = -1 is the vertical asymptote.  Also notice that if x grows increasingly large, the fraction shown tends towards x/x, or 1, so we know that the horizontal asymptote is y = 1.

Draw a set of x-y axes and graph y = 1 and x = -1.  Plot (0, 0).  Again, note that the graph of this function never touches/crosses x = -1.  So, for (-1, 0) the graph is a curve caught between x = -1 and x = 0 that increases as x increases.  For (0, infinity), the graph heads upward at a slow pace and then levels off nearly parallel to y = 1 (the horizontal asymptote).

As x increases from left to right, y starts out slightly greater than y = 1 and then (while still in Quadrant II) curves upward and approaches the vertical asymptote x = -1.