Hey there!

The idea of infinity in math can seem a bit confusing, but it's actually really interesting. Let’s break it down into simple parts:

1. Limits at Infinity:

This is all about how a function behaves when it gets really, really big.

For example, if we look at the function $f(x) = \frac{1}{x}$, as $x$ gets larger and larger (approaching infinity), the limit gets closer to $0$.

So, in simple terms, the function gets smaller and smaller as $x$ gets bigger.

2. Vertical Asymptotes:

These happen when a function goes up or down really fast, almost to infinity.

Take the function $f(x) = \frac{1}{x-1}$.

As $x$ gets closer to $1$, the limit shoots up towards infinity.

This means the function jumps very high when you get near that number.

So, it’s all about how functions behave when they reach extreme values! Pretty cool, right?