document.write( "Question 126942This question is from textbook Thinking Mathematically
\n" ); document.write( ": a.) Graph f(x)=3^x
\n" ); document.write( "b.) Evaluate 2f(-0.125) \n" ); document.write( "

Algebra.Com's Answer #92977 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
a)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3%5Ex\"$ Start with the given function\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%280%29=3%5E0\"$ Plug in $\"x=0\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1\"$ Raise 3 to the zeroth power to get 1\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , $\"y=1\"$ . So our first point is (0,1)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----Now lets find another point----
\n" ); document.write( " $\"f%281%29=3%5E1\"$ Plug in $\"x=1\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%281%29=3\"$ Raise 3 to the first power to get 3\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"y=3\"$ . So our second point is (1,3)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----Now lets find another point----
\n" ); document.write( " $\"f%282%29=3%5E2\"$ Plug in $\"x=2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%282%29=9\"$ Raise 3 to the second power to get 9\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"y=9\"$ . So our third point is (2,9)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "===============================================================================\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now lets make a table of the values we have calculated\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( " x y
 0 1
 1 3
 2 9\r\n" );
document.write( "

Now plot the points\r
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Connect the points with a smooth curve to form the graph $\"y=3%5Ex\"$ (note: the more points you plot, the easier it is to graph)\r
\n" ); document.write( "\n" ); document.write( "

Graph of $\"y=3%5Ex\"$ through the points solved for earlier\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3%5Ex\"$ Start with the given function\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28-0.125%29=3%5E%28-0.125%29\"$ Plug in $\"x=-0.125\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%28-0.125%29=0.8717\"$ Use a calculator to evaluate $\"3%5E%28-0.125%29\"$ to get 0.8717\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2%2Af%28-0.125%29=2%2A0.8717\"$ Now multiply both sides by 2\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2%2Af%28-0.125%29=1.7434\"$ Multiply\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );