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

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03-05-2021
Mathematics

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

Sagot :

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Altavistardidn Altavistardidn · Answer 1 · 2021-05-04T12:53:07-04:00

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.

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