document.write( "Question 92199This question is from textbook Algebra and Trigonometry
\n" ); document.write( ": (a) Graph the function f(x)= x^3 - 4
\n" ); document.write( "(b) Approximate to the nearest tenth, the real root of the equation
\n" ); document.write( " f(x)= x^3 - 4 = 0 please help me \n" ); document.write( "

Algebra.Com's Answer #67029 by jim_thompson5910(35256) $\"\"$ $\"About$

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a) \"Graph the function f(x)= x^3 - 4\"\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=x%5E3-4\"$ , we need to plot some points.
\n" ); document.write( "We can start at any x value, so lets start at x=-2\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%28-2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3-4\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%28-2%29%5E3-4\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%28-8%29-4\"$ Raise -2 to the third power to get -8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-12\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , $\"f%28-2%29=-12\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-2,-12)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%28-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3-4\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%28-1%29%5E3-4\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%28-1%29-4\"$ Raise -1 to the third power to get -1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-5\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , $\"f%28-1%29=-5\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-1,-5)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%280%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3-4\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29%5E3-4\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280%29-4\"$ Raise 0 to the third power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=4\"$ Remove any zero terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , $\"f%280%29=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (0,-4)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%281%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3-4\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%5E3-4\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29-4\"$ Raise 1 to the third power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"f%281%29=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (1,-3)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%282%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3-4\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%282%29%5E3-4\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%288%29-4\"$ Raise 2 to the third power to get 8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=4\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"f%282%29=4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (2,4)\r
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\n" ); document.write( "\n" ); document.write( "Now lets make a table of the values we have calculated\r
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document.write( " x y
 -2 -12
 -1 -5
 0 -4
 1 -3
 2 4\r\n" );
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Now plot the points\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=x%5E3-4\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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\n" ); document.write( "\n" ); document.write( "b)\r
\n" ); document.write( "\n" ); document.write( "\"approximate to the nearest tenth, the real root of the equation
\n" ); document.write( " f(x)= x^3 - 4 = 0 \"\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E3+-+4+=+0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E3+=+4\"$ add 4 to both sides\r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+root%283%2C4%29\"$ Take the cube root of both sides\r
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\n" ); document.write( "\n" ); document.write( "So the solution is approximately 1.5874010519682 which rounds to 1.6 \n" ); document.write( "

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