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# a) What is the domain of the function ?

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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
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(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
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a) -8

CuteDramione  Jun 22, 2019
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Yes. Then the domain is every real number except -8.

MaxWong  Jun 22, 2019
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so a is anything but 0?

EDIT: i meant -8... whoops

CuteDramione  Jun 22, 2019
edited by CuteDramione  Jun 22, 2019
#5
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More accurately, it's every real number except -8.

MaxWong  Jun 22, 2019
#6
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ahhhh.... whoops. Im saying whoops alot today... :(

CuteDramione  Jun 22, 2019
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(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   Jun 22, 2019
#8
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(c)         x^2

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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 )   Jun 22, 2019
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NIOCE CPHILL

CuteDramione  Jun 22, 2019