Question 143189
{{{f(x)=5^x}}} Start with the given expression

In order to plot an exponential function, we need to plot some points

We can start at any x value, so lets start at x=-1


{{{f(-1)=5^(-1)}}}  Plug in {{{x=-1}}}


{{{f(-1)=1/5}}}  Raise 5  to the negative first power to get {{{1/5}}} or {{{0.2}}}


So when {{{x=0}}}, {{{y=0.2}}}. So our  first point is (-1,0.2)



----Now lets find another point----


{{{f(0)=5^0}}}  Plug in {{{x=0}}}


{{{f(0)=1}}}  Raise 5  to the zeroth power to get 1


So when {{{x=0}}}, {{{y=1}}}. So our  second point is (0,1)



----Now lets find another point----
{{{f(1)=5^1}}}  Plug in {{{x=1}}}


{{{f(1)=5}}}  Raise 5  to the first power to get 5


So when {{{x=1}}}, {{{y=5}}}. So our  third point is (1,5)



----Now lets find another point----
{{{f(2)=5^2}}}  Plug in {{{x=2}}}


{{{f(2)=25}}}  Raise 5  to the second power to get 25


So when {{{x=2}}}, {{{y=25}}}. So our  fourth point is (2,25)




===============================================================================


Now lets make a table of the values we have calculated

<pre>
<TABLE width=500>

<TR><TD> x</TD><TD>y</TD></TR>
<TR><TD> -1</TD><TD>0.2</TD></TR>
<TR><TD> 0</TD><TD>1</TD></TR> 
<TR><TD> 1</TD><TD>5</TD></TR> 
<TR><TD> 2</TD><TD>25</TD></TR> 
</TABLE>
</pre>Now plot the points

{{{drawing( 900, 900, -10, 10, -10, 10,
  grid( 1 ),
circle(-1,0.2,0.05),
circle(-1,0.2,0.08),
circle(0,1,0.05),
circle(0,1,0.08),
circle(1,5,0.05),
circle(1,5,0.08),
circle(2,25,0.05),
circle(2,25,0.08),
circle(3,125,0.05),
circle(3,125,0.08))}}}



Connect the points to form the graph {{{y=5^x}}}

{{{drawing( 900, 900, -10, 10, -10, 10,
grid( 1 ),
graph( 900, 900, -10, 10, -10, 10, 5^x),
circle(-1,0.2,0.05),
circle(-1,0.2,0.08),
circle(0,1,0.05),
circle(0,1,0.08),
circle(1,5,0.05),
circle(1,5,0.08),
circle(2,25,0.05),
circle(2,25,0.08),
circle(3,125,0.05),
circle(3,125,0.08))}}} Graph of {{{y=5^x}}} through the points solved for earlier