Question 150386
I'll do the first two to get you started.


# 1


Table of Contents:
<a name="top1">
<a href="#table1">Table</a>

<a href="#graph1">Graph</a>


In order to graph {{{y=7^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. 



{{{y=7^x}}} Start with the given equation.



{{{y=7^-2}}} Plug in {{{x=-2}}}.




{{{y=1/7^2}}} Rewrite {{{7^-2}}} as {{{1/7^2}}}



{{{y=1/49}}} Evaluate {{{7^2}}} to get 49



{{{y=0.02}}} Divide and simplify.



So when {{{x=-2}}}, {{{y=0.02}}}. So we have the point (-2,0.02).



----------------------------



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



{{{y=7^x}}} Start with the given equation.



{{{y=7^-1}}} Plug in {{{x=-1}}}.



{{{y=1/7^1}}} Rewrite {{{7^-1}}} as {{{1/7^1}}}



{{{y=1/7}}} Evaluate {{{7^1}}} to get 7



{{{y=0.143}}} Divide and simplify.



So when {{{x=-1}}}, {{{y=0.143}}}. So we have the point (-1,0.143).



----------------------------



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



{{{y=7^x}}} Start with the given equation.



{{{y=7^0}}} Plug in {{{x=0}}}.



{{{y=1}}} Evaluate {{{7^0}}} to get 1 



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



----------------------------



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



{{{y=7^x}}} Start with the given equation.



{{{y=7^1}}} Plug in {{{x=1}}}.



{{{y=7}}} Evaluate {{{7^1}}} to get 7 



So when {{{x=1}}}, {{{y=7}}}. So we have the point (1,7).



----------------------------



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



<a name="table1">



<a href="#top1">Jump to Table of Contents</a>

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

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR>TEST: -2
<tr><td>-2</td><td>0.02</td></tr>
<tr><td>-1</td><td>0.143</td></tr>
<tr><td>0</td><td>1</td></tr>
<tr><td>1</td><td>7</td></tr>
</TABLE>

</pre>

Now let's plot these points:



{{{ drawing(900, 900, -10, 10, -10, 10,
grid(1),
graph(900, 900, -10, 10, -10, 10, 0),
circle(-2,0.02,0.08),circle(-2,0.02,0.10),
circle(-1,0.143,0.08),circle(-1,0.143,0.10),
circle(0,1,0.08),circle(0,1,0.10),
circle(1,7,0.08),circle(1,7,0.10)

)}}}


<a name="graph1">



<a href="#top1">Jump to Table of Contents</a>

<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=7^x}}}:



{{{ drawing(900, 900, -10, 10, -10, 10,
grid(1),
graph(900, 900, -10, 10, -10, 10, 7^x),
circle(-2,0.02,0.08),circle(-2,0.02,0.10),
circle(-1,0.143,0.08),circle(-1,0.143,0.10),
circle(0,1,0.08),circle(0,1,0.10),
circle(1,7,0.08),circle(1,7,0.10)

)}}} Graph of {{{y=7^x}}}



<hr>


# 2


Table of Contents:
<a name="top2">
<a href="#table2">Table</a>

<a href="#graph2">Graph</a>


In order to graph {{{y=4^(x-3)}}}, we need to plot a few points.



Let's find the y value when {{{x=0}}} note: you can start at any x value. 



{{{y=4^(x-3)}}} Start with the given equation.



{{{y=4^(0-3)}}} Plug in {{{x=0}}}.



{{{y=4^(-3)}}} Subtract



{{{y=1/4^3}}} Rewrite {{{4^(-3)}}} as {{{1/4^3}}}



{{{y=1/64}}} Evaluate {{{4^3}}} to get {{{64}}}



{{{y=0.016}}} Divide and simplify.



So when {{{x=0}}}, {{{y=0.016}}}. So we have the point (0,0.016).



----------------------------



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



{{{y=4^(x-3)}}} Start with the given equation.



{{{y=4^(1-3)}}} Plug in {{{x=1}}}.



{{{y=4^(-2)}}} Subtract



{{{y=1/4^2}}} Rewrite {{{4^(-2)}}} as {{{1/4^2}}}



{{{y=1/16}}} Evaluate {{{4^2}}} to get {{{16}}}



{{{y=0.063}}} Divide and simplify.



So when {{{x=1}}}, {{{y=0.063}}}. So we have the point (1,0.063).



----------------------------



Let's find the y value when {{{x=2}}}  



{{{y=4^(x-3)}}} Start with the given equation.



{{{y=4^(2-3)}}} Plug in {{{x=2}}}.



{{{y=4^(-1)}}} Subtract



{{{y=1/4^1}}} Rewrite {{{4^(-1)}}} as {{{1/4^1}}}



{{{y=1/4}}} Evaluate {{{4^1}}} to get {{{4}}}



{{{y=0.25}}} Divide and simplify.



So when {{{x=2}}}, {{{y=0.25}}}. So we have the point (2,0.25).



----------------------------



Let's find the y value when {{{x=3}}}  



{{{y=4^(x-3)}}} Start with the given equation.



{{{y=4^(3-3)}}} Plug in {{{x=3}}}.




{{{y=4^(0)}}} Subtract



{{{y=1}}} Evaluate {{{4^0}}} to get {{{1}}}



So when {{{x=3}}}, {{{y=1}}}. So we have the point (3,1).



----------------------------



Let's find the y value when {{{x=4}}}  



{{{y=4^(x-3)}}} Start with the given equation.



{{{y=4^(4-3)}}} Plug in {{{x=4}}}.



{{{y=4^(1)}}} Subtract



{{{y=4}}} Evaluate {{{4^1}}} to get {{{4}}}



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



----------------------------



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



<a name="table2">



<a href="#top2">Jump to Table of Contents</a>

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

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR>TEST: 0
<tr><td>0</td><td>0.016</td></tr>
<tr><td>1</td><td>0.063</td></tr>
<tr><td>2</td><td>0.25</td></tr>
<tr><td>3</td><td>1</td></tr>
<tr><td>4</td><td>4</td></tr>
</TABLE>

</pre>

Now let's plot these points:



{{{ drawing(900, 900, -7, 7, -7, 7,
grid(1),
graph(900, 900, -7, 7, -7, 7, 0),
circle(0,0.016,0.05),circle(0,0.016,0.08),
circle(1,0.063,0.05),circle(1,0.063,0.08),
circle(2,0.25,0.05),circle(2,0.25,0.08),
circle(3,1,0.05),circle(3,1,0.08),
circle(4,4,0.05),circle(4,4,0.08)

)}}}


<a name="graph2">



<a href="#top2">Jump to Table of Contents</a>

<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=4^(x-3)}}}:



{{{ drawing(900, 900, -7, 7, -7, 7,
grid(1),
graph(900, 900, -7, 7, -7, 7, 4^(x-3)),
circle(0,0.016,0.05),circle(0,0.016,0.08),
circle(1,0.063,0.05),circle(1,0.063,0.08),
circle(2,0.25,0.05),circle(2,0.25,0.08),
circle(3,1,0.05),circle(3,1,0.08),
circle(4,4,0.05),circle(4,4,0.08)

)}}} Graph of {{{y=4^(x-3)}}}