help with how to sketch vertical and horizontal asymptotes

[mdem1234]

Hi

The question is :

Sketch the graph of y = ?1/x-2 +3, identifying any vertical or horizontal asymptotes.

So would I be right in saying that there is a vertical asymptote of x= -2, because this would make the denominator add to zero? And I'm not 100 % sure on how I would sketch this? and how can I tell the difference between a horizontal and a vertical asymptote? I understand the difference but am not sure how you can tell which is which from an equation.

Any help would be awesome, Thanks!

 

[think.ms.tink]

x=2 would be a vertical asymptote where u draw a dashed line on that point, because that is where the graph will not exist. it would be vertical because it is where x does not exist. also create a table of values to help you draw the graph.

 

[BigGlenntheHeavy]

f(x) = -1/(x-2)+3. When x = 2, f(x) is undefined so x=2 is a vertical asymptote.

Lim f(x) = 3 so y= 3 is a horizontal asymptote.
x-> + or - infinity

Hence x=2 and y=3 are the two asymptotes.

 

[mdem1234]

Thanks guys, that makes more sense, I dont know why I thought it was -2

Sorry for my ignorance but how did you get that the limit for f(x) = 3 ?

 

[stapel]

how did you get that the limit for f(x) = 3 ?

Convert the second term (the "plus three") to the common denominator, combine the two terms, and then use what you learned back in algebra about horizontal asymptotes or what you learned in calculus about limits. :wink: