Question

What is the vertical asymptote for the graph of
y = x-2/(x-2)(x+3)?

Answer 1

i think that its x=-3 and x=2 ? right?

Answer 2

There is an ambiguity with the rational function, not sure if it is
\(\large y = \frac{x-2}{(x-2)(x+3)}\) or \(\large y = \frac{(x-2)}{(x-2)}(x+3)\)
According to the rule PEMDAS, it's the second, but I think you meant the first.

Answer 3

Hint: simplify the rational function before attempting to locate asymptotes.

Answer 4

It's the first equation

Answer 5

Good, so follow the hints and see where they take you!

Answer 6

I did simplify thats how I got x = -3

Answer 7

What is the simplified version of the function, and what do you think the graph looks like?

Answer 8

i think there is a hole so the answer might be (2, 1/5) ?

Answer 9

Very good, the hole is at (2,1/5).
Where do you think the asymptotes are?

Answer 10

The function is now:
f(x)=1/(x+3) where x\(\ne\)2
the hole (x=2) is not part of the domain.

Answer 11

hint:
Try to visualize where the asymptotes should be. If not ,use your graphs calculator

Answer 12

Remember that an asymptote occurs when the denominator becomes zero.