Question 206133
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^3+2x^2 = 0}}}
- first factor if possible
- {{{(x^2)(x+2) = 0}}}
- then set each factor to zero and solve for x
- {{{x^2 = 0}}} and {{{x+2 = 0}}}
- {{{sqrt(x^2) = sqrt(0)}}} and {{{x+2-2 = 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 {{{(-infinity * infinity)}}} (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...
- {{{(-infinity * -2)}}},{{{(-2 * 0)}}},{{{(0 * infinity)}}} (replace the dots with commas by the way)
And that's you answer