Sandwich Theorem

Question

Suppose that  𝑔(𝑥)≤𝑓(𝑥)≤ℎ(𝑥) for all 𝑥's near  𝑥=𝑐, and that  lim𝑥→𝑐𝑔(𝑥)=𝐾 ,  lim𝑥→𝑐𝑓(𝑥)=𝑀 and  lim𝑥→𝑐ℎ(𝑥)=𝑁 .

The Sandwich Theorem says that...

Group of answer choices

1. 𝐾=𝑀=𝑁
2. 𝐾<𝑀<𝑁
3. If  𝐾=𝑀 , then  𝐾=𝑀=𝑁
4. If  𝐾=𝑁 , then 𝐾=𝑀=𝑁 
5. If  𝑀=𝑁, then  𝐾=𝑀=𝑁

Answer 1

Let's draw a little picture of a POSSIBLE scenario here. We are told that (near "c") g(x) has the smallest values, f(x) has values in the middle, and h(x) has the largest values. So a graph could look like this:

Notice the reason the call it the "sandwich" theorem (looks like two pieces of bread with some sandwich material in the middle). I typically have heard it called the Squeeze Theorem (f(x) is getting squeezed between g(x) and h(x)).

So, which answer is it then?