document.write( "Question 57793: Given f(x)=(x+1)^2(x-1)(x+2)(x+4)^3
\n" ); document.write( "a.) Find the x- and y- intercepts of f.
\n" ); document.write( "b.) Determine whether the graph touches or crosses the x-axis at each x-intercept. How do you do this without graphing f?
\n" ); document.write( "c.) What power function does f resemble for very large values of |x|? \n" ); document.write( "

Algebra.Com's Answer #39504 by stanbon(75887) $\"\"$ $\"About$

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Given f(x)=(x+1)^2(x-1)(x+2)(x+4)^3
\n" ); document.write( "a.) Find the x- and y- intercepts of f.
\n" ); document.write( "For y-int let x=0, then y=1^2*-1*2*4^3=-48
\n" ); document.write( "For x-int: x=-1 of multiplicity 2; 1 mult 1; -2 mult 1; -4 mult 3
\n" ); document.write( "b.) Determine whether the graph touches or crosses the x-axis at each x-intercept. How do you do this without graphing f?
\n" ); document.write( "If the multiplicity is even the curve touches but does not cross the x-axis
\n" ); document.write( "at that x value; if the multiplicity is odd the graph passes through the
\n" ); document.write( "x axis at that x value.
\n" ); document.write( "c.) What power function does f resemble for very large values of |x|?
\n" ); document.write( "f(x)=x^7
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( " \n" ); document.write( "

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