Describing the behaviour of a function? (1 Viewer)

[sadpwner]

Describe the behaviour of f(x)=1+ (1/x) as x tends to positive and negative infinity.

I am assuming the answer is: As x->infinity y->1 and as x->-infinity y->1

Is this correct?

Also, describe the behaviour of the function f(x)=1+ (1/x) around x=0.

Not sure about this one.
There isn't a wealth of information regarding this so wondering if anyone can help.

 

[Queenroot]

bump SR

 

[seventhroot]

So using limits, you're on the right track

So what happens when x gets arbitrarily large? The function approaches 1+ likewise when x gets arbitrary large for negative values the function approaches 1-. We can see that y = 1 is a horizontal asympote because f(x) can never equal 1

Furthermore, at x = 0; there is a vertical asympote because x can also never equal zero. If we take a left hand limit, we can see that the function tends towards negative infinity conversely if we take the right hand limit, f(x) approaches positive infinity

 

[Queenroot]

I swear this isn't even in 2u

 

[seventhroot]

I swear this isn't even in 2u

IT Is on the verge of harder 2U maybe some of 3U. This is used a lot in 4U graphs

 

[mohammy52]

Definitely 2U

 

[integral95]

HSC maths doesn't even teach the concept of 2 sided limits.........

 

[seventhroot]

HSC maths doesn't even teach the concept of 2 sided limits.........

iirc; 4U does

 

[braintic]

Definitely 2U

It has never been tested in a 2U HSC exam beyond horizontal asymptotes. And those graphs are just hyperbolae that are learned in the functions topic before the idea of limits is taught.

 

[panda15]

iirc; 4U does

Don't you need to know 2-sided limits for 3U graphs?

 

[seventhroot]

Don't you need to know 2-sided limits for 3U graphs?

yes I agree but it is used all the time in 4U like to determine the behaviour of a function close to asympotes and stuff