Question

How did they find out ×=2 is an asymptote?? This is really confusing and frustrating!

d C 4{ ,al 44% 7:41 PM We should start by looking at the points where either the numerator or denominator is 0. The numerator is zero if r 1-0, which means z--1. Similarly, the denominator is zero if x-2-0, which means x = 2 . Plotting these points on the number line, we get the following There is an asymptote at 2, so we use an open circle there. Because the inequality is not strict, it allows for values of x where the function is 0, so we use a closed circle (filled in circle) for Now, we choose a test point from each region above. Let's use x-2, r0, and x 3. (-2)-24 ะ 0.25 Because 0.25 > 0, the point 2 makes the inequality false, and so every value in this region will not satisfy the inequality At 0: (0+1 1 (0) -22 -0.5

Answer 1

A vertical Asymptote is defined as x = , if

So, if in a rational function f(x) / g(x) if
_{f(a)メ0, and g(a)=0. then}

f (a) g(a)

In this case x = is a vertical asymptote.

Here, we have

for x=2 is = 2+1 2-2 T-2

OR, we can simply compare denominator to zero which gives x-2 = 0

So, x = 2 is a vertical asymptote.