document.write( "Question 211246: Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Use the resulting ordered pairs to plot the graph of each function.\r
\n" ); document.write( "\n" ); document.write( "So for this problem there will be two lines on one graph? How do I plot the points? I'm really lost on this one and any help would be appreciated. I'd also be willing to pay a tutor for help on this! Please contact me if interested! Thanks. \n" ); document.write( "

Algebra.Com's Answer #159614 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Well it helps to have the entire problem. What is the given function?\r
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\n" ); document.write( "\n" ); document.write( "If you're having problems graphing in general, here's an example:\r
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\n" ); document.write( "\n" ); document.write( "Problem: Graph $\"y=2%5Ex\"$ \r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=2%5Ex\"$ , we need to plot a few points.\r
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\n" ); document.write( "\n" ); document.write( "To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-2\"$ note: you can start at any x value. \r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%28-2%29\"$ Plug in $\"x=-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.25\"$ Evaluate $\"2%5E%28-2%29\"$ to get $\"0.25\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-2\"$ , then $\"y=0.25\"$ which gives us the point (-2,0.25).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-1.5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%28-1.5%29\"$ Plug in $\"x=-1.5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.354\"$ Evaluate $\"2%5E%28-1.5%29\"$ to get $\"0.354\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-1.5\"$ , then $\"y=0.354\"$ which gives us the point (-1.5,0.354).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-1\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%28-1%29\"$ Plug in $\"x=-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.5\"$ Evaluate $\"2%5E%28-1%29\"$ to get $\"0.5\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-1\"$ , then $\"y=0.5\"$ which gives us the point (-1,0.5).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-0.5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%28-0.5%29\"$ Plug in $\"x=-0.5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.707\"$ Evaluate $\"2%5E%28-0.5%29\"$ to get $\"0.707\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-0.5\"$ , then $\"y=0.707\"$ which gives us the point (-0.5,0.707).\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=0.5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%280.5%29\"$ Plug in $\"x=0.5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1.414\"$ Evaluate $\"2%5E%280.5%29\"$ to get $\"1.414\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=0.5\"$ , then $\"y=1.414\"$ which gives us the point (0.5,1.414).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%281%29\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2\"$ Evaluate $\"2%5E%281%29\"$ to get $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=2\"$ which gives us the point (1,2).\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=1.5\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%281.5%29\"$ Plug in $\"x=1.5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2.828\"$ Evaluate $\"2%5E%281.5%29\"$ to get $\"2.828\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=1.5\"$ , then $\"y=2.828\"$ which gives us the point (1.5,2.828).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%282%29\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4\"$ Evaluate $\"2%5E%282%29\"$ to get $\"4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=4\"$ which gives us the point (2,4).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=2.5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%282.5%29\"$ Plug in $\"x=2.5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=5.657\"$ Evaluate $\"2%5E%282.5%29\"$ to get $\"5.657\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=2.5\"$ , then $\"y=5.657\"$ which gives us the point (2.5,5.657).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5Ex\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%5E%283%29\"$ Plug in $\"x=3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=8\"$ Evaluate $\"2%5E%283%29\"$ to get $\"8\"$ \r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=3\"$ , then $\"y=8\"$ which gives us the point (3,8).\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 0.25
-1.5 0.354
-1 0.5
-0.5 0.707
0.5 1.414
1 2
1.5 2.828
2 4
2.5 5.657
3 8\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:

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

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