document.write( "Question 130638: Sketch the graph of the function $\"f%28x%29=%282%2F3%29%5Ex\"$ \n" ); document.write( "

Algebra.Com's Answer #95402 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In order to graph $\"f%28x%29=%282%2F3%29%5Ex\"$ , 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( " $\"f%28x%29=%282%2F3%29%5Ex\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=%282%2F3%29%5E%28-5%29\"$ Plug in $\"x=-5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=%280.666666666666667%29%5E%28-5%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-5%29=%280.666666666666667%29%5E%28-5%29\"$ Raise 0.666666666666667 to the negative 5th power to get 7.59374999999998\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-5\"$ , we have $\"y=7.59374999999998\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-5,7.59374999999998)\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( " $\"f%28x%29=%282%2F3%29%5Ex\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%282%2F3%29%5E%28-4%29\"$ Plug in $\"x=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%280.666666666666667%29%5E%28-4%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=%280.666666666666667%29%5E%28-4%29\"$ Raise 0.666666666666667 to the negative 4th power to get 5.06249999999999\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-4\"$ , we have $\"y=5.06249999999999\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-4,5.06249999999999)\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( " $\"f%28x%29=%282%2F3%29%5Ex\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%282%2F3%29%5E%28-3%29\"$ Plug in $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%280.666666666666667%29%5E%28-3%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=%280.666666666666667%29%5E%28-3%29\"$ Raise 0.666666666666667 to the negative 3rd power to get 3.375\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-3\"$ , we have $\"y=3.375\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (-3,3.375)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%282%2F3%29%5Ex\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%282%2F3%29%5E%28-2%29\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%280.666666666666667%29%5E%28-2%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=%280.666666666666667%29%5E%28-2%29\"$ Raise 0.666666666666667 to the negative 2nd power to get 2.25\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , we have $\"y=2.25\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (-2,2.25)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%282%2F3%29%5Ex\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%282%2F3%29%5E%28-1%29\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%280.666666666666667%29%5E%28-1%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=%280.666666666666667%29%5E%28-1%29\"$ Raise 0.666666666666667 to the negative 1st power to get 1.5\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=1.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (-1,1.5)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%282%2F3%29%5E%280%29\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280.666666666666667%29%5E%280%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=%280.666666666666667%29%5E%280%29\"$ Raise 0.666666666666667 to the 0th power to get 1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 6th point is (0,1)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%282%2F3%29%5E%281%29\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%280.666666666666667%29%5E%281%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%280.666666666666667%29%5E%281%29\"$ Raise 0.666666666666667 to the 1st power to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=0.666666666666667\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 7th point is (1,0.666666666666667)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%282%2F3%29%5E%282%29\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%280.666666666666667%29%5E%282%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%280.666666666666667%29%5E%282%29\"$ Raise 0.666666666666667 to the 2nd power to get 0.444444444444445\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , we have $\"y=0.444444444444445\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 8th point is (2,0.444444444444445)\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( " $\"f%283%29=%282%2F3%29%5E%283%29\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%280.666666666666667%29%5E%283%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%280.666666666666667%29%5E%283%29\"$ Raise 0.666666666666667 to the 3rd power to get 0.296296296296297\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , we have $\"y=0.296296296296297\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 9th point is (3,0.296296296296297)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=%282%2F3%29%5E%284%29\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=%280.666666666666667%29%5E%284%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=%280.666666666666667%29%5E%284%29\"$ Raise 0.666666666666667 to the 4th power to get 0.197530864197531\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , we have $\"y=0.197530864197531\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 10th point is (4,0.197530864197531)\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( " $\"f%285%29=%282%2F3%29%5E%285%29\"$ Plug in $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=%280.666666666666667%29%5E%285%29\"$ Divide 3 into 2 to get 0.666666666666667\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=%280.666666666666667%29%5E%285%29\"$ Raise 0.666666666666667 to the 5th power to get 0.131687242798354\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , we have $\"y=0.131687242798354\"$ \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
 -5 7.59374999999998
 -4 5.06249999999999
 -3 3.375
 -2 2.25
 -1 1.5
 0 1
 1 0.666666666666667
 2 0.444444444444445
 3 0.296296296296297
 4 0.197530864197531
 5 0.131687242798354\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 $\"y=%282%2F3%29%5Ex\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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