document.write( "Question 130693: Graph the following. Label all x-intercepts, y-intercepts, and any asymptotes.\r
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Algebra.Com's Answer #95434 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In order to graph $\"f%28x%29=2%5Ex-4\"$ , we need to plot some points. To do that, we need to plug in some x values to get some y values\r
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\n" ); document.write( "\n" ); document.write( "So let's find the first point:\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=2%5Ex-4\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=2%5E%280%29-4\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1-4\"$ Raise 2 to the 0th power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-3\"$ Subtract 4 from 1 to get -3\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (0,-3)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=2%5Ex-4\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=2%5E%281%29-4\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=2-4\"$ Raise 2 to the 1st power to get 2\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-2\"$ Subtract 4 from 2 to get -2\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (1,-2)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=2%5Ex-4\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=2%5E%282%29-4\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=4-4\"$ Raise 2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=0\"$ Subtract 4 from 4 to get 0\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , we have $\"y=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (2,0)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=2%5Ex-4\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=2%5E%283%29-4\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=8-4\"$ Raise 2 to the 3rd power to get 8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=4\"$ Subtract 4 from 8 to get 4\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , we have $\"y=4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (3,4)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=2%5E%284%29-4\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=16-4\"$ Raise 2 to the 4th power to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=12\"$ Subtract 4 from 16 to get 12\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , we have $\"y=12\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (4,12)\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
 0 -3
 1 -2
 2 0
 3 4
 4 12\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 $\"y=2%5Ex-4\"$ (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( "By looking at the graph, we can note the following\r
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\n" ); document.write( "\n" ); document.write( "y-intercept: (0,-3)\r
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\n" ); document.write( "\n" ); document.write( "Horizontal Asymptote(s): $\"y=-4\"$ (ie a horizontal line at the y value of -4)\r
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\n" ); document.write( "\n" ); document.write( "Vertical Asymptote(s): none (ie the graph continues on forever in both directions along the x-axis) \n" ); document.write( "

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