document.write( "Question 1075131: A curve has equation y = (x^2-5x+7)/(x-3).
\n" ); document.write( "Find the range of y for real x. Hence, or otherwise, find the coordinates of the turning points. \n" ); document.write( "

Algebra.Com's Answer #689845 by Boreal(15235) $\"\"$ $\"About$

You can put this solution on YOUR website!
y = (x^2-5x+7)/(x-3)
\n" ); document.write( "If x=0, y=-7/3
\n" ); document.write( "if x is infinite positive, y is infinite positive
\n" ); document.write( "If x is infinite negative, y is infinite negative
\n" ); document.write( "Can y=0?
\n" ); document.write( "No, because the discriminant, when you set the expression equal to 0 and multiply by x-3, is negative.
\n" ); document.write( "The derivative is (x^2-6x+8)/(x-3)^2. If you set that equal to 0, x equals 2 and 4.
\n" ); document.write( "As x approaches 3 from the positive side, y approaches + infinity.
\n" ); document.write( "As x approaches 3 from the negative side, y approaches - infinity.
\n" ); document.write( "The turning points are at x=2 and x=4, where y= -1 and and 3 respectively (2,-1) and (4, 3)
\n" ); document.write( "The range is (-oo,-1] and [3,oo)
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%5E2-5x%2B7%29%2F%28x-3%29%29\"$ \n" ); document.write( "

\n" );