SwaGGeReR

Which of the following is an asymptote of f(x) = [(x^2 + 3x + 2)/(x+2)]*tan(pi*x)?

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.

Clarification please?

jerrry4445

if u factor x^2+3x+2, it'll be x+2 and x+1. So, after simplifying, you have (x+1)*tan(pi*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.

Vale!

^he said the answer is x=1/2 not x=-1/2

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

SwaGGeReR

ahh, I forgot to factor out the numerator. Thanks guys!

listzt

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).

Whatever floats your boat for solving the problem, though