Question 151076
Is the equation {{{y=6^x-5}}}?



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

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


In order to graph {{{y=6^x-5}}}, we need to plot a few points.



Let's find the y value when {{{x=-1}}} note: you can start at any x value. 



{{{y=6^x-5}}} Start with the given equation.



{{{y=6^-1-5}}} Plug in {{{x=-1}}}.



{{{y=-4.833}}} Evaluate the right side with a calculator.



So when {{{x=-1}}}, {{{y=-4.833}}}. So we have the point (-1,-4.833).



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



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



{{{y=6^x-5}}} Start with the given equation.



{{{y=6^0-5}}} Plug in {{{x=0}}}.



{{{y=-4}}} Evaluate the right side with a calculator.



So when {{{x=0}}}, {{{y=-4}}}. So we have the point (0,-4).



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



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



{{{y=6^x-5}}} Start with the given equation.



{{{y=6^1-5}}} Plug in {{{x=1}}}.



{{{y=1}}} Evaluate the right side with a calculator.



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



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



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



<a name="table1">



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

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR><tr><td>-1</td><td>-4.833</td></tr>
<tr><td>0</td><td>-4</td></tr>
<tr><td>1</td><td>1</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(900, 900, -10, 10, -10, 10,
grid(1),
graph(900, 900, -10, 10, -10, 10, 0),
circle(-1,-4.833,0.08),circle(-1,-4.833,0.10),
circle(0,-4,0.08),circle(0,-4,0.10),
circle(1,1,0.08),circle(1,1,0.10)

)}}}


<a name="graph1">



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<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=6^x-5}}}:



{{{ drawing(900, 900, -10, 10, -10, 10,
grid(1),
graph(900, 900, -10, 10, -10, 10, 6^x-5),
circle(-1,-4.833,0.08),circle(-1,-4.833,0.10),
circle(0,-4,0.08),circle(0,-4,0.10),
circle(1,1,0.08),circle(1,1,0.10)

)}}} Graph of {{{y=6^x-5}}}



<hr>


Or....


Is the equation {{{y=6^(x-5)}}}??





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

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


In order to graph {{{y=6^(x-5)}}}, we need to plot a few points.



Let's find the y value when {{{x=3}}} note: you can start at any x value. 



{{{y=6^(x-5)}}} Start with the given equation.



{{{y=6^(3-5)}}} Plug in {{{x=3}}}.



{{{y=0.028}}} Evaluate the right side with a calculator.



So when {{{x=3}}}, {{{y=0.028}}}. So we have the point (3,0.028).



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



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



{{{y=6^(x-5)}}} Start with the given equation.



{{{y=6^(4-5)}}} Plug in {{{x=4}}}.



{{{y=0.167}}} Evaluate the right side with a calculator.



So when {{{x=4}}}, {{{y=0.167}}}. So we have the point (4,0.167).



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



Let's find the y value when {{{x=5}}}  



{{{y=6^(x-5)}}} Start with the given equation.



{{{y=6^(5-5)}}} Plug in {{{x=5}}}.



{{{y=1}}} Evaluate the right side with a calculator.



So when {{{x=5}}}, {{{y=1}}}. So we have the point (5,1).



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



Let's find the y value when {{{x=6}}}  



{{{y=6^(x-5)}}} Start with the given equation.



{{{y=6^(6-5)}}} Plug in {{{x=6}}}.



{{{y=6}}} Evaluate the right side with a calculator.



So when {{{x=6}}}, {{{y=6}}}. So we have the point (6,6).



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



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



<a name="table2">



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

<TABLE border="1" width="100">
<TR><TD>x</TD><TD>y</TD></TR><tr><td>3</td><td>0.028</td></tr>
<tr><td>4</td><td>0.167</td></tr>
<tr><td>5</td><td>1</td></tr>
<tr><td>6</td><td>6</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(900, 900, -10, 10, -10, 10,
grid(1),
graph(900, 900, -10, 10, -10, 10, 0),
circle(3,0.028,0.08),circle(3,0.028,0.10),
circle(4,0.167,0.08),circle(4,0.167,0.10),
circle(5,1,0.08),circle(5,1,0.10),
circle(6,6,0.08),circle(6,6,0.10)

)}}}


<a name="graph2">



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<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=6^(x-5)}}}:



{{{ drawing(900, 900, -10, 10, -10, 10,
grid(1),
graph(900, 900, -10, 10, -10, 10, 6^(x-5)),
circle(3,0.028,0.08),circle(3,0.028,0.10),
circle(4,0.167,0.08),circle(4,0.167,0.10),
circle(5,1,0.08),circle(5,1,0.10),
circle(6,6,0.08),circle(6,6,0.10)

)}}} Graph of {{{y=6^(x-5)}}}