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What is the range of the function $g(x) = \frac{3x+1}{x+8} + \frac{2x-4}{x+8}$ ?

 Aug 4, 2023
 #1
avatar+129197 
+1

Simplify as

[ 3x + 1 + 2x - 4]  / [ x + 8]   =

 

[ 5x - 3 ] / [ x + 8]

 

This function has a horizontal  asymptote at   y =   (the ratio of the coefficients on x ) = 5/1 = 5 

 

The range is  (-inf, 5) U (5, inf)

 

cool cool cool

 Aug 5, 2023
 #2
avatar+198 
+2

well well well, looks like someone's back!...

Welcome back CPhill!...smiley

icecreamlover  Aug 5, 2023
 #3
avatar+129197 
+1

Thanks, icecreamlover !!!!

 

 

cool cool cool

CPhill  Aug 5, 2023

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