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1. help find the equations of the asymptotes for the function  f(x) .

 

f(x)=−2/x+4   (to the side of the fraction)−6

Vertical asymptote: ___________

Horizontal asymptote:__________

 

2.

(Pretty easy, just not sure if I am doing it the right way yet.)

What are the domain and range of the function?

f(x)=  3sqrt x−3

 

Domain: (3, ∞)

Range: (0, ∞)

 

Domain: [3, ∞)

Range: [0, ∞)

 

Domain: [3, ∞)

Range: (−∞, ∞)

 

Domain: (3, ∞)

Range: (3, ∞)

 

Thanks a million!

 Feb 14, 2019
 #1
avatar+104756 
+2

First one

 

-2 / ( x + 4)

 

Whatever x value makes the denominator 0 is a vertical asymptote....this is x = - 4

 

We hav e a lower degree polynomial  /  higher degree polynomial

 

Whenever this is the case, we will have a horizontal asymptote at y = 0

 

Second one

 

f(x) =  3 sqrt (x - 3)

 

The square root cannot be negative...so    x - 3 ≥ 0  ⇒    x ≥ 3

So....the domain is  [ 3, infinity )

 

The smallest y value occurs when  x = 0......this will lead to   3 sqrt (3 - 3) = 3sqrt (0)  = 0

And the function is aways increasing to infinity as x increases

 

So....the range is [ 0 , infinity )

 

 

cool cool cool

 Feb 14, 2019

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