+73 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.
+9673 (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 \((-\infty ,0]\).
+129852 (b) 3x + 1
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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
+129852 (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 )
