1. Question on Infinity

Just a random question I've been wondering about after my functions class today. The lesson was on sketching functions, so just finding the x-intercepts and y-intercepts. We also did this thing with infinity to determine which end went up and which end went down on a cubic function or w.e. It would be something like this...

y= (x+2)(x-1)(x+3)
xints= -3,-2,1
yint= -6

When x approaches infinity
y also approaches infinity

For this we would subsitute in infinity in for x and it would remain positive so the right side of the function would go up and therefore the left side down...

So finally to my question : Would there ever be a time when x approaches infinity that y approaches negative infinity? So that the right side of the function goes downwards instead of upwards? If so what would the circumstances be in the factored form of the equation?

Sorry if this is confusing I'm just curious

Thanks

2. Originally Posted by Shout

So finally to my question : Would there ever be a time when x approaches infinity that y approaches negative infinity? So that the right side of the function goes downwards instead of upwards? If so what would the circumstances be in the factored form of the equation?
There are many examples, here's one.

$y = -x^3$

3. Originally Posted by Shout
Just a random question I've been wondering about after my functions class today. The lesson was on sketching functions, so just finding the x-intercepts and y-intercepts. We also did this thing with infinity to determine which end went up and which end went down on a cubic function or w.e. It would be something like this...

y= (x+2)(x-1)(x+3)
xints= -3,-2,1
yint= -6

When x approaches infinity
y also approaches infinity

For this we would subsitute in infinity in for x and it would remain positive so the right side of the function would go up and therefore the left side down...

So finally to my question : Would there ever be a time when x approaches infinity that y approaches negative infinity? So that the right side of the function goes downwards instead of upwards? If so what would the circumstances be in the factored form of the equation?

Sorry if this is confusing I'm just curious

Thanks
Just change the sign on any one of the x's and the constant in any of the three factors you've written.

The graph "flips" upside-down.