Posted by Calculus on Saturday, October 31, 2009 at 10:05pm.
I'm asked to find the domain of fuction
(x+5)/(x3)
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

(x3)/x
(1+5/X)

(13/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)

(x3)

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)

(13/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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