What are the asymptotes for $((x+2)(x+5))/(x+2)$ ?

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Answer 1 · 2015-08-07T19:03:19

There are no vertical or horizontal asymptotes

$y=((x+2)(x+5))/(x+2)$

Step 1. Cross out any factors in both the numerator and denominator.

$y=color(red)(cancel(color(black)("("x+2")"))color(black)("("x+5")"))/color(red)cancel(color(black)(x+2)$

This reduces the function to the line $y=x+5$ with a removable discontinuity (a little hole in the graph) where $x=-2$ and $y=-2+5=3$ .

So the hole is at (-2,3).

Step 2. Find the vertical asymptotes.

Since the denominator is now 1, there are no vertical asymptotes.

Step 3. Find the horizontal asymptotes.

This is a linear equation. There are no horizontal asymptotes.

There are no horizontal or vertical asymptotes.

Graph.

What are the asymptotes for ((x+2)(x+5))/(x+2)((x+2)(x+5))/(x+2)?