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Given this function: f(x) =3/[x+3]  -9

 

explain how you'd  identify the vertical asymptote of the function without graphing.

 

 

identify the horizontal asymptote of the function writing the entire equation

 

also can you explain how to identify the horizontal asymptote of the function without graphing.

 Feb 19, 2019
 #1
avatar+104836 
+3

f(x) =  3 / { x + 3] - 9

 

The vertical  asymptote is the value of x that makes the denominator = 0

 

So....

 

x + 3 =  0

 

x = - 3   ⇒   vertical asymptote

 

 

To find the horizontal asymptote.....note that       3/ [ x +3 ]   is a lower power polynomial / higher power polynomial

 

When we have this situation, the horizontal asymptote is y = 0

 

However .....   the "-9"   at the end actually shifts this horizontal aymptote DOWN by 9 units

 

So....the horizontal asymptote is y = - 9

 

Here's the graph :   https://www.desmos.com/calculator/93af4udovt

 

 

cool cool cool

 Feb 19, 2019
edited by CPhill  Feb 19, 2019

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