Homework Help Forum: Calculus

Posted by Calculus on Saturday, October 31, 2009 at 10:05pm.

I'm asked to find the domain of fuction (x+5)/(x-3) saying that x is all reals except for x can not equal three is wrong correct? Because i can evalue function when x = 3 as follows 3 + 5 = 8 so saying that the function has range x is a reals except x can not equal three is wrong because it can???

• Calculus - jim, Saturday, October 31, 2009 at 10:13pm

  No, it's not wrong. When x=3, we have: (x + 5) / ( x - 3) = (3 + 5) / ( 3 - 3) = 8 / 0 which is undefined, because of division by zero.

  
  

• Calculus - Calculus , Saturday, October 31, 2009 at 10:15pm

  no its 8

  
  

• HELP - HELP, Saturday, October 31, 2009 at 10:16pm

  I'm sure i did it right

  
  

• Calculus - jim, Saturday, October 31, 2009 at 10:25pm

  What is 8 divided by zero?

  
  

• Calculus - HELP, Saturday, October 31, 2009 at 10:34pm

  no... also all reals is wrong because i know you can never get a value greater than -5/3

  
  

• Calculus - HELP, Saturday, October 31, 2009 at 10:45pm

  wait what am I doing wrong here (X+5)/(X - 3) (x+5)/x -------- (x-3)/x (1+5/X) -------- (1-3/x) i forgot were to go from here

  
  

• Calculus - jim, Saturday, October 31, 2009 at 10:47pm

  (x+5)/(x - 3) is just (x+5) ----- (x-3)

  
  

• Calculus - HELP, Saturday, October 31, 2009 at 10:51pm

  1 + 0 ------------- 1 - 0 I'm just getting 1????

  
  

• Calculus - HELP, Saturday, October 31, 2009 at 10:53pm

  oh... I did it right graph it if you don't believe me

  
  

• Calculus - HELP, Saturday, October 31, 2009 at 10:55pm

  so the range is... y is... arg confused

  
  

• Calculus - HELP, Saturday, October 31, 2009 at 10:57pm

  ...every number except 1?

  
  

• Calculus - HELP, Saturday, October 31, 2009 at 11:11pm

  So how come we can not say that x can not equal 3 because I'm getting 8 when x = 3 also how come we say range is all reals when its not because y will never equal 1

  
  

• Calculus - Reiny, Sunday, November 1, 2009 at 7:28am

  To the person posting as "Help" The reply by Jim is correct, division by zero is undefined and causes a vertical asymptote in the corresponding graph for the given function. Changing it to the form (1+5/X) -------- (1-3/x) serves no purpose, since when x = 3 you are still dividing by zero. Changing it to that form would be useful if we wanted to find the horizontal asymptote, by letting x become "very large". We can see that the above would approach 1 and the H.A. would be y = 1 As stated by jim, the domain is the set of real numbers, except x cannot be 3 .

  
  

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