Question 181965
I'll graph the first function {{{y=4^x}}}. This will point you to the right graph for the first one (and the second one by elimination). However, you can use the same techniques to get the graph of the second function.



Let's graph {{{y=4^x}}}




In order to graph {{{y=4^x}}}, we need to plot a few points.



Let's find the y value when {{{x=-2}}} note: you can start at any x value. 



{{{f(x)=4^x}}} Start with the given equation.



{{{f(-2)=4^-2}}} Plug in {{{x=-2}}}.



{{{f(-2)=0.063}}} Evaluate the right side (with a calculator).



So when {{{x=-2}}}, {{{y=0.063}}}. So we have the point (-2,0.063).



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Let's find the y value when {{{x=-1}}}  



{{{f(x)=4^x}}} Start with the given equation.



{{{f(-1)=4^-1}}} Plug in {{{x=-1}}}.



{{{f(-1)=0.25}}} Evaluate the right side (with a calculator).



So when {{{x=-1}}}, {{{y=0.25}}}. So we have the point (-1,0.25).



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Let's find the y value when {{{x=0}}}  



{{{f(x)=4^x}}} Start with the given equation.



{{{f(0)=4^0}}} Plug in {{{x=0}}}.



{{{f(0)=1}}} Evaluate the right side (with a calculator).



So when {{{x=0}}}, {{{y=1}}}. So we have the point (0,1).



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Let's find the y value when {{{x=1}}}  



{{{f(x)=4^x}}} Start with the given equation.



{{{f(1)=4^1}}} Plug in {{{x=1}}}.



{{{f(1)=4}}} Evaluate the right side (with a calculator).



So when {{{x=1}}}, {{{y=4}}}. So we have the point (1,4).



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Now let's make a table of the values we just found.



<h4>Table of Values:</h4><pre>

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR><tr><td>-2</td><td>0.063</td></tr>
<tr><td>-1</td><td>0.25</td></tr>
<tr><td>0</td><td>1</td></tr>
<tr><td>1</td><td>4</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(900, 900, -7, 7, -7, 7,
grid(1),
graph(900, 900, -7, 7, -7, 7, 0),
circle(-2,0.063,0.08),circle(-2,0.063,0.10),circle(-2,0.063,0.05),
circle(-1,0.25,0.08),circle(-1,0.25,0.10),circle(-1,0.25,0.05),
circle(0,1,0.08),circle(0,1,0.10),circle(0,1,0.05),
circle(1,4,0.08),circle(1,4,0.10),circle(1,4,0.05)

)}}}


<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=4^x}}}:



{{{ drawing(900, 900, -7, 7, -7, 7,
grid(1),
graph(900, 900, -7, 7, -7, 7, 4^x),
circle(-2,0.063,0.08),circle(-2,0.063,0.10),circle(-2,0.063,0.05),
circle(-1,0.25,0.08),circle(-1,0.25,0.10),circle(-1,0.25,0.05),
circle(0,1,0.08),circle(0,1,0.10),circle(0,1,0.05),
circle(1,4,0.08),circle(1,4,0.10),circle(1,4,0.05)

)}}} Graph of {{{y=4^x}}}