document.write( "Question 173237: I've been working on my homework and I have it all finished except for two graphing problems. I was wondering how to plot the graphs of the following functions:
\n" ); document.write( "f(x)=(1/5)^x
\n" ); document.write( "f(x)=4^x - 3
\n" ); document.write( "f(x)=7^x \n" ); document.write( "

Algebra.Com's Answer #128045 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll do the first two to get you started.\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"f%28x%29=%281%2F5%29%5Ex\"$ , we need to plot some points:\r
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\n" ); document.write( "\n" ); document.write( "Note: I'll use \"y\" in place of f(x)\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( " $\"y=%281%2F5%29%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5E%28-1%29\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%285%2F1%29%5E1\"$ Flip the fraction to make the exponent positive.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%285%29%5E1\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( " $\"y=5\"$ Raise $\"5\"$ to the first power to get 5\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , then $\"y=5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5E0\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1\"$ Raise $\"1%2F5\"$ to the zeroth power to get 1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , then $\"y=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "-----------------------------------------------\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5E1\"$ Plug in $\"x=1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2F5\"$ Raise $\"1%2F5\"$ to the first power to get $\"1%2F5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.2\"$ Divide\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , then $\"y=0.2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5E2\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2F25\"$ Square $\"1%2F5\"$ to get $\"%281%2F5%29%5E2=%281%2F5%29%281%2F5%29=1%2F25\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.04\"$ Divide\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , then $\"y=0.04\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5E3\"$ Plug in $\"x=3\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2F125\"$ Cube $\"1%2F5\"$ to get $\"%281%2F5%29%5E3=%281%2F5%29%281%2F5%29%281%2F5%29=1%2F125\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.008\"$ Divide\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , then $\"y=0.008\"$ \r
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\n" ); document.write( "\n" ); document.write( "-----------------------------------------------\r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5Ex\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%2F5%29%5E4\"$ Plug in $\"x=4\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2F625\"$ Raise $\"1%2F5\"$ to the fourth power to get $\"%281%2F5%29%5E4=%281%2F5%29%281%2F5%29%281%2F5%29%281%2F5%29=1%2F625\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.0016\"$ Divide\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , then $\"y=0.0016\"$ \r
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\n" ); document.write( "\n" ); document.write( "So we have the following values:\r
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x	y
-1	5
0	1
1	0.2
2	0.04
3	0.08
4	0.0016

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\n" ); document.write( "\n" ); document.write( "Now let's plot these points\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now draw a curve through those points to graph $\"f%28x%29=%281%2F5%29%5Ex\"$ \r
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\r
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\n" ); document.write( "\n" ); document.write( "Note: the graph does NOT cross or touch the x-axis. It just looks like that since the y values become very small.\r
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\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 $\"f%28x%29=4%5E%28x-3%29\"$ , we need to plot some points:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: I'll use \"y\" in place of f(x)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28x-3%29\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%280-3%29\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28-3%29\"$ Subtract\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2F4%5E%283%29\"$ Flip the fraction to make the exponent positive\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2F64\"$ Cube 4 to get 64\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.015625\"$ Divide.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , then $\"y=0.015625\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28x-3%29\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%281-3%29\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28-2%29\"$ Subtract\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2F4%5E%282%29\"$ Flip the fraction to make the exponent positive\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2F16\"$ Square 4 to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.0625\"$ Divide.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , then $\"y=0.0625\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28x-3%29\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%282-3%29\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28-1%29\"$ Subtract\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1%2F4%5E%281%29\"$ Flip the fraction to make the exponent positive\r
\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2F4\"$ Raise 4 to the first power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0.25\"$ Divide.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , then $\"y=0.25\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28x-3%29\"$ Start with the given equation\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%283-3%29\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%280%29\"$ Subtract\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1\"$ Raise 4 to the zeroth power to get 1\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , then $\"y=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28x-3%29\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%284-3%29\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%281%29\"$ Subtract\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4\"$ Raise 4 to the first power to get 4\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , then $\"y=4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y value when $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%28x-3%29\"$ Start with the given equation\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%285-3%29\"$ Plug in $\"x=5\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4%5E%282%29\"$ Subtract\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16\"$ Square 4 to get 16\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , then $\"y=16\"$ \r
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\n" ); document.write( "\n" ); document.write( "So we have the following values:\r
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x	y
0	0.015625
1	0.0625
2	0.25
3	1
4	4
5	16

\r
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\n" ); document.write( "\n" ); document.write( "Now draw a curve through those points to graph $\"f%28x%29=4%5E%28x-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "Note: once again, the graph does NOT cross or touch the x-axis. It just looks like that since the y values start off very small. \n" ); document.write( "

\n" );