Question

f(x) = 1/x^2
Identify any horizontal and vertical asymptotes and identify any holes in the graph.

Answer 1

What value of x would lead to a zero in the denominator?

Answer 2

0?

Answer 3

Yes. So if x cannot equal zero, x = 0 must either be a hole or an asymptote. Do you know which it is?

Answer 4

I think it's an asymptote.

Answer 5

Yes, exactly. If it were a hole, it would've been canceled out. You've got your answer.

Answer 6

What about horizontal asymptotes?
And how can I tell if there is a hole?

Answer 7

@greenglasses How can I tell if there's a horizontal asymptote?

Answer 8

Oh right, I missed the horizontal asymptote part.

Answer 9

Right, firstly, if there was a hole, you would've cancelled out a value: for example, in the equation: \[f(x)=\frac{ (x+1) }{ (x+1)(x+2)}\]

Answer 10

x cannot equal -1 or -2, but since you can cancel out x = 1 from the numerator and denominator, x= -1 would be the hole and x = -2 would be the asymptote

Answer 11

I usually use limits to find a horizontal asymptote- do you know what that is?

Answer 12

No, but my teacher gave me this rule:
Big Top, no asymptote
Big Bottom, y=0
BS (I forgot which one it stood for) ex. 4x/3x, y=4/3

Answer 13

Yes, in this case, the graph has a 'big bottom', and y = 0.

Answer 14

That's what I thought. May I ask how I would use limits in this situation?

Answer 15

If you don't know what they are, you probably shouldn't worry about it. Your teacher will teach you eventually if you're in Pre-Calc.

Answer 16

OK, thank you!