SOLUTION: The section we are currently working on in class is titled "Rational Expressions and Functions." The directions for the problems are to 'Find all values of the variable for which t

Algebra ->  Functions -> SOLUTION: The section we are currently working on in class is titled "Rational Expressions and Functions." The directions for the problems are to 'Find all values of the variable for which t      Log On


   

Question 206133: The section we are currently working on in class is titled "Rational Expressions and Functions." The directions for the problems are to 'Find all values of the variable for which the given rational function is undefined. Then express the domain in interval notation.' Unfortunately some of the equations are more complex. How do I go about solving such a problem as this one:
%285x-3%29%2F%28x%5E3%2B2x%5E2%29
Found 2 solutions by Marth, Targetweek:
Answer by Marth(57) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%285x-3%29%2F%28x%5E3%2B2x%5E2%29
The function is undefined when the denominator equals 0.



Set the denominator equal to 0.
0=x%5E3+%2B+2x%5E2
Factor.
0+=+x%5E2%28x%2B2%29
x%5E2=0
x+=+0
_________
+x%2B2+=+0+
x+=+-2
__________
The function is defined for all x except x = 0,-2
So the interval notation is (-infinity, -2) U (-2, 0) U (0, infinity)

Answer by Targetweek(62) About Me  (Show Source):
You can put this solution on YOUR website!
Well To dind all the values of the variable for which the given rational function is defined we have to know why it would be undefined
- When the denominatot is 0 then the function is undefined because you can't divide by 0
- So set the denominator equal to 0
- x%5E3%2B2x%5E2+=+0
- first factor if possible
- %28x%5E2%29%28x%2B2%29+=+0
- then set each factor to zero and solve for x
- x%5E2+=+0 and x%2B2+=+0
- sqrt%28x%5E2%29+=+sqrt%280%29 and x%2B2-2+=+0-2
- x+=+0 and x=-2
- So when x = 0,-2 the function is undefined
- The values are x=0,-2
- hopefully you already understand how to use interval notation
- If not here's a quick explanation (sorry if it doesn't make sense, u should ask your math teacher)
- ex. any graph in the y=mx+b form will have the notation of %28-infinity+%2A+infinity%29 (put a comma between them) because the x-values of the graph never stop in either direction
- However other functions do have ending points and the such
- a "(" is used to say up to this value but not including it like an open circle on a number line or piecewise graph
- a "[" is used like a closed circle on a number line or piecewise function
- Now that that's over back to business
- Because the the only x values that don't exist in this function or where the function is undefined are 0 and -2 so...
- %28-infinity+%2A+-2%29,%28-2+%2A+0%29,%280+%2A+infinity%29 (replace the dots with commas by the way)
And that's you answer