document.write( "Question 181968: Plot the graphs of the following functions. \r
\n" ); document.write( "\n" ); document.write( "f(x) = 5^x
\n" ); document.write( "f(x) = 4^x+2
\n" ); document.write( "f(x) = (1/3)^x
\n" ); document.write( "f(x) = log5x (I'm not sure how to format the \"5\", It's more like a smaller 5 that is lower and in between the g and the x)\r
\n" ); document.write( "\n" ); document.write( "I asked this question previously, But I realized the formatting didn't transfer over. thanks for all the help \n" ); document.write( "

Algebra.Com's Answer #136586 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
To graph ANY function, simply follow this basic routine:\r
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\n" ); document.write( "\n" ); document.write( "1) Plug in any x value to find it's corresponding function value (or y value). This gives you an ordered pair (x,y)\r
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\n" ); document.write( "\n" ); document.write( "2) Plot the points that you calculated from step 1\r
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\n" ); document.write( "\n" ); document.write( "3) Draw a smooth connected through ALL of the points that you plotted in step 2\r
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\n" ); document.write( "\n" ); document.write( "I'll do the first two to get you started. The other two follow the same basic outline.\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=5%5Ex\"$ , we need to plot a few points.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=5%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=5%5E%28-2%29\"$ Plug in $\"x=-2\"$ (note: you can start at any x-value).\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=0.04\"$ Raise 5 to the -2nd power to get $\"0.04\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , $\"y=0.04\"$ . So we have the point (-2,0.04).\r
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\n" ); document.write( "\n" ); document.write( "----------------------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=5%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=5%5E%28-1%29\"$ Plug in $\"x=-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=0.2\"$ Raise 5 to the -1st power to get $\"0.2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , $\"y=0.2\"$ . So we have the point (-1,0.2).\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=5%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=5%5E%280%29\"$ Plug in $\"x=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1\"$ Raise 5 to the 0th power to get $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , $\"y=1\"$ . So we have the point (0,1).\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=5%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=5%5E%281%29\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=5\"$ Raise 5 to the 1st power to get $\"5\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"y=5\"$ . So we have the point (1,5).\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
-2 0.04
-1 0.2
0 1
1 5\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\r
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Graph:

\r
\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=5%5Ex\"$ :\r
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Graph of $\"y=5%5Ex\"$ \r
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\n" ); document.write( "\n" ); document.write( "# 2\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=4%5E%28x%2B2%29\"$ , we need to plot a few points.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=4%5E%28x%2B2%29\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=4%5E%28-4%2B2%29\"$ Plug in $\"x=-4\"$ (note: you can start at any x-value).\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=4%5E%28-2%29\"$ Add.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-4%29=0.063\"$ Raise 4 to the -2nd power to get $\"0.063\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-4\"$ , $\"y=0.063\"$ . So we have the point (-4,0.063).\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=4%5E%28x%2B2%29\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=4%5E%28-3%2B2%29\"$ Plug in $\"x=-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=4%5E%28-1%29\"$ Add.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-3%29=0.25\"$ Raise 4 to the -1st power to get $\"0.25\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-3\"$ , $\"y=0.25\"$ . So we have the point (-3,0.25).\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=4%5E%28x%2B2%29\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=4%5E%28-2%2B2%29\"$ Plug in $\"x=-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=4%5E%280%29\"$ Add.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=1\"$ Raise 4 to the 0th power to get $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , $\"y=1\"$ . So we have the point (-2,1).\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=4%5E%28x%2B2%29\"$ Start with the given equation.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=4%5E%28-1%2B2%29\"$ Plug in $\"x=-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=4%5E%281%29\"$ Add.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=4\"$ Raise 4 to the 1st power to get $\"4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , $\"y=4\"$ . So we have the point (-1,4).\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
-4 0.063
-3 0.25
-2 1
-1 4\r\n" );
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\r
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\r
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Graph:

\r
\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=4%5E%28x%2B2%29\"$ :\r
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Graph of $\"y=4%5E%28x%2B2%29\"$ \n" ); document.write( "

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