SOLUTION: I need an equation that has a domain of [-4, 5/3) U (5/3, infinity) if you could at least walk me through how to find it, that would be great.

Question 220294: I need an equation that has a domain of [-4, 5/3) U (5/3, infinity)
if you could at least walk me through how to find it, that would be great.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
5/3 can't be part of the domain.
If you divide by (3x-5) then when x = (5/3) you will be dividing by 0 because 3*(5/3) - 5 = 5-5 = 0.
That makes x = (5/3) not part of the domain.
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Your equation will be something divided by (x-5/3).
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Now we need to restrict your domain to values of x >= -4
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We can do that with square root of something that makes the something inside the square root negative when x < -4.
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Equation of should do it.
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When x < -4, expression within the square root sign is negative. This forces the domain to be >= -4.
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When x = 5/3, denominator is 0 causing value of the equation to be undefined. This forces the domain to exclude x = 5/3.
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Graph of this equation is shown below:

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Table of Values from x = -10 to x = 10 are shown below:
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x_______________y
-10____________#NUM!
-9____________#NUM!
-8____________#NUM!
-7____________#NUM!
-6____________#NUM!
-5____________#NUM!
-4____________0
-3____________-0.071428571
-2____________-0.128564869
-1____________-0.216506351
0____________-0.4
1____________-1.118033989
(5/3)________#DIV/0!
2____________2.449489743
3____________0.661437828
4____________0.404061018
5____________0.3
6____________0.243252128
7____________0.207289049
8____________0.182321138
9____________0.163888694
10____________0.149666295

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