document.write( "Question 1001667: What is each piece of information telling about the function exactly?\r
\n" ); document.write( "\n" ); document.write( "The function has these properites:
\n" ); document.write( "f(0) = 0
\n" ); document.write( "f'(1) = 0
\n" ); document.write( "lim x->∞ f(x) = 0
\n" ); document.write( "lim x->-∞ f(x) = 0
\n" ); document.write( "lim x->-1 f(x) = ∞
\n" ); document.write( "f'(x)>0 on (-∞,-1)U(1,∞)
\n" ); document.write( "f'(x)<0 on (-1,1)
\n" ); document.write( "f\"(x)>0 on (-∞,-1)U(-1,3)
\n" ); document.write( "f\"(x)<0 on (3,∞)\r
\n" ); document.write( "\n" ); document.write( "Please explain these have an exam and I need to know how to construct a graph from this information.\r
\n" ); document.write( "\n" ); document.write( "Thank you\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #618890 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

Statement	Translation
f(0) = 0	The point (0,0) is on the graph of f(x)
f'(1) = 0	The slope of the tangent line at x = 1 is m = 0. This tangent line is horizontal
lim x->∞ f(x) = 0	There is a horizontal asymptote at y = 0
lim x->-∞ f(x) = 0	There is a horizontal asymptote at y = 0
lim x->-1 f(x) = ∞	There is a vertical asymptote at x = -1
f'(x)>0 on (-∞,-1)U(1,∞)	Function f(x) is increasing when x < -1 or when x > 1
f'(x)<0 on (-1,1)	Function f(x) is decreasing when -1 < x < 1
f\"(x)>0 on (-∞,-1)U(-1,3)	Function f(x) is concave up when x < -1 or when -1 < x < 3
f\"(x)<0 on (3,∞)	Function f(x) is concave down when x > 3

\n" ); document.write( "

\n" );