<p>Which of the following is an asymptote of f(x) = [(x^2 + 3x + 2)/(x+2)]<em>tan(pi</em>x)?</p>
<p>I put x=-2 since when you plug in -2 for x, the denominator is equal to zero. Also, the graph is undefined at x=-2. However, Barron's says the answer is x=1/2, but doesn't really explain why--it just says look at the graph.</p>
<p>Clarification please?</p>
<p>if u factor x^2+3x+2, it’ll be x+2 and x+1. So, after simplifying, you have (x+1)<em>tan(pi</em>x). the reason why it’s -1/2 because tan (-pi/2) does not exist. you could see that when u input that on your calculator.</p>
<p>^he said the answer is x=1/2 not x=-1/2</p>
<p>but you do have to factor out the numerator to cancel out (x+2). In order for the function to be undefined, tan of theta must be undefined, which can only be true if x is 1/2 making theta= to 90 degrees or pi/2</p>
<p>ahh, I forgot to factor out the numerator. Thanks guys!</p>
<p>Just to clarify where the Barron’s answer is coming from, x = -2 is a point discontinuity. If you look at the graph, there isn’t an asymptote there (it approaches a single value from both the positive and negative x axes).</p>
<p>Whatever floats your boat for solving the problem, though :)</p>