document.write( "Question 117748: sketch the graph of the following functions
\n" ); document.write( "f(x)=-2*(3)^x and g(x)=4*(1/3)^x \n" ); document.write( "

Algebra.Com's Answer #85734 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll do the first one to show you how to do these\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-2%2A3%5Ex\"$ Start with the given expression\r
\n" ); document.write( "\n" ); document.write( "In order to plot an exponential function, we need to plot some points\r
\n" ); document.write( "\n" ); document.write( "We can start at any x value, so lets start at x=0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-2%2A3%5E0\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-2%2A1\"$ Raise 3 to the zeroth power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-2\"$ Multiply -2 by 1 to get -2\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , $\"y=-2\"$ . So our first point is (0,-2)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----
\n" ); document.write( " $\"f%281%29=-2%2A3%5E1\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-2%2A3\"$ Raise 3 to the first power to get 3\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-6\"$ Multiply -2 by 3 to get 6\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"y=-6\"$ . So our second point is (1,-6)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----
\n" ); document.write( " $\"f%282%29=-2%2A3%5E2\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-2%2A9\"$ Raise 3 to the second power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-18\"$ Multiply -2 by 9 to get -18\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"y=-18\"$ . So our third point is (2,-18)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----
\n" ); document.write( " $\"f%283%29=-2%2A3%5E3\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-2%2A27\"$ Raise 3 to the third power to get 27\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-54\"$ Multiply -2 by 27 to get -54\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , $\"y=-54\"$ . So our fourth point is (3,-54)\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 -2
 1 -6
 2 -18
 3 -54\r\n" );
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Now plot the points\r
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\n" ); document.write( "\n" ); document.write( "Connect the points to form the graph $\"y=-2%2A3%5Ex\"$ \r
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Graph of $\"y=-2%2A3%5Ex\"$ through the points solved for earlier \n" ); document.write( "

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