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avatar+64 

a) What is the domain of the function \(g(x) = \frac{3x+1}{x+8}?\) ?

b) What is the range of the function  \(g(x) = \frac{3x+1}{x+8}\)?

c)The domain of the function \(r(x) = \frac{x^2}{1-x}\ is\ (-\infty,1)\cup(1,\infty)\) . What is the range?
 Hellp me, dont give me all of the answer, just give me a nudge.

 Jun 22, 2019
 #1
avatar+7677 
0

(a) Think about what makes the fraction undefined. What value(s) of x makes the denominator 0?

(b) Notice that the function has a vertical asymptote. Substitute points around the vertical asymptote to find out if the range is \((-\infty,\infty)\)\((-\infty ,0)\),\((0,\infty)\),\([0,\infty)\), or \((-\infty ,0]\).

(c) Notice that the function has a vertical asymptote. Substitute points around the vertical asymptote to find out if the range is \((-\infty,\infty)\)\((-\infty ,0)\),\((0,\infty)\),\([0,\infty)\), or \((-\infty ,0]\)​.

 Jun 22, 2019
 #2
avatar+64 
-2

a) -8

CuteDramione  Jun 22, 2019
 #3
avatar+7677 
+1

Yes. Then the domain is every real number except -8.

MaxWong  Jun 22, 2019
 #4
avatar+64 
-2

so a is anything but 0?

 

EDIT: i meant -8... whoops

CuteDramione  Jun 22, 2019
edited by CuteDramione  Jun 22, 2019
 #5
avatar+7677 
+1

More accurately, it's every real number except -8.

MaxWong  Jun 22, 2019
 #6
avatar+64 
-4

ahhhh.... whoops. Im saying whoops alot today... :(

CuteDramione  Jun 22, 2019
 #7
avatar+101813 
+2

(b)         3x + 1

             ______

               x + 8

 

We  have     a   same degree polynomial  / same degree polynomial......this means that we will have a horizontal asymptote    at   y   =    ratio of  the coefficients on x  in the numerator/denominator  

 

So....the horizontal asymptote occurs  at     y  =  3 / 1  =  3

 

So...the range will be   (-infinity, 3)   and  (3, infinity )

 

Check the graph, here :   https://www.desmos.com/calculator/umaqjrwwtr

 

cool cool cool

 Jun 22, 2019
 #8
avatar+101813 
+2

(c)         x^2

          ______

            1  -  x

 

Unfortunately....other than a graph, we will need to use some Calculus to find the range..this is a little involved, but not that difficult....hence.....the graph might be the best way to go :

 

https://www.desmos.com/calculator/vdr0itmcy5

 

The graph shows that the range is  (-inf, 4]   and [ 0, inf )

 

 

cool cool cool

 Jun 22, 2019
 #9
avatar+64 
-4

NIOCE CPHILL

CuteDramione  Jun 22, 2019

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