Question 211246
Well it helps to have the entire problem. What is the given function?



If you're having problems graphing in general, here's an example:



Problem: Graph {{{y=2^x}}}



Solution:




In order to graph {{{y=2^x}}}, we need to plot a few points.



To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.



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



{{{y=2^x}}} Start with the given equation.



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



{{{y=0.25}}} Evaluate {{{2^(-2)}}} to get {{{0.25}}}



So if {{{x=-2}}}, then {{{y=0.25}}} which gives us the point (-2,0.25).



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



Let's find the y value when {{{x=-1.5}}}  



{{{y=2^x}}} Start with the given equation.



{{{y=2^(-1.5)}}} Plug in {{{x=-1.5}}}.



{{{y=0.354}}} Evaluate {{{2^(-1.5)}}} to get {{{0.354}}}



So if {{{x=-1.5}}}, then {{{y=0.354}}} which gives us the point (-1.5,0.354).



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



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



{{{y=2^x}}} Start with the given equation.



{{{y=2^(-1)}}} Plug in {{{x=-1}}}.



{{{y=0.5}}} Evaluate {{{2^(-1)}}} to get {{{0.5}}}



So if {{{x=-1}}}, then {{{y=0.5}}} which gives us the point (-1,0.5).



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



Let's find the y value when {{{x=-0.5}}}  



{{{y=2^x}}} Start with the given equation.



{{{y=2^(-0.5)}}} Plug in {{{x=-0.5}}}.



{{{y=0.707}}} Evaluate {{{2^(-0.5)}}} to get {{{0.707}}}



So if {{{x=-0.5}}}, then {{{y=0.707}}} which gives us the point (-0.5,0.707).



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



Let's find the y value when {{{x=0.5}}}  



{{{y=2^x}}} Start with the given equation.



{{{y=2^(0.5)}}} Plug in {{{x=0.5}}}.



{{{y=1.414}}} Evaluate {{{2^(0.5)}}} to get {{{1.414}}}



So if {{{x=0.5}}}, then {{{y=1.414}}} which gives us the point (0.5,1.414).



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



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



{{{y=2^x}}} Start with the given equation.



{{{y=2^(1)}}} Plug in {{{x=1}}}.



{{{y=2}}} Evaluate {{{2^(1)}}} to get {{{2}}}



So if {{{x=1}}}, then {{{y=2}}} which gives us the point (1,2).



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



Let's find the y value when {{{x=1.5}}}  



{{{y=2^x}}} Start with the given equation.



{{{y=2^(1.5)}}} Plug in {{{x=1.5}}}.



{{{y=2.828}}} Evaluate {{{2^(1.5)}}} to get {{{2.828}}}



So if {{{x=1.5}}}, then {{{y=2.828}}} which gives us the point (1.5,2.828).



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



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



{{{y=2^x}}} Start with the given equation.



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



{{{y=4}}} Evaluate {{{2^(2)}}} to get {{{4}}}



So if {{{x=2}}}, then {{{y=4}}} which gives us the point (2,4).



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



Let's find the y value when {{{x=2.5}}}  



{{{y=2^x}}} Start with the given equation.



{{{y=2^(2.5)}}} Plug in {{{x=2.5}}}.



{{{y=5.657}}} Evaluate {{{2^(2.5)}}} to get {{{5.657}}}



So if {{{x=2.5}}}, then {{{y=5.657}}} which gives us the point (2.5,5.657).



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



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



{{{y=2^x}}} Start with the given equation.



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



{{{y=8}}} Evaluate {{{2^(3)}}} to get {{{8}}}



So if {{{x=3}}}, then {{{y=8}}} which gives us the point (3,8).



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



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>0.25</td></tr>
<tr><td>-1.5</td><td>0.354</td></tr>
<tr><td>-1</td><td>0.5</td></tr>
<tr><td>-0.5</td><td>0.707</td></tr>
<tr><td>0.5</td><td>1.414</td></tr>
<tr><td>1</td><td>2</td></tr>
<tr><td>1.5</td><td>2.828</td></tr>
<tr><td>2</td><td>4</td></tr>
<tr><td>2.5</td><td>5.657</td></tr>
<tr><td>3</td><td>8</td></tr>
</TABLE>

</pre>

Now let's plot the points:



{{{ drawing(500, 500, -10, 10, -10, 10,
grid(1),
graph(500, 500, -10, 10, -10, 10, 0),
circle(-2,0.25,0.08),circle(-2,0.25,0.10),circle(-2,0.25,0.12),circle(-2,0.25,0.14),
circle(-1.5,0.354,0.08),circle(-1.5,0.354,0.10),circle(-1.5,0.354,0.12),circle(-1.5,0.354,0.14),
circle(-1,0.5,0.08),circle(-1,0.5,0.10),circle(-1,0.5,0.12),circle(-1,0.5,0.14),
circle(-0.5,0.707,0.08),circle(-0.5,0.707,0.10),circle(-0.5,0.707,0.12),circle(-0.5,0.707,0.14),
circle(0.5,1.414,0.08),circle(0.5,1.414,0.10),circle(0.5,1.414,0.12),circle(0.5,1.414,0.14),
circle(1,2,0.08),circle(1,2,0.10),circle(1,2,0.12),circle(1,2,0.14),
circle(1.5,2.828,0.08),circle(1.5,2.828,0.10),circle(1.5,2.828,0.12),circle(1.5,2.828,0.14),
circle(2,4,0.08),circle(2,4,0.10),circle(2,4,0.12),circle(2,4,0.14),
circle(2.5,5.657,0.08),circle(2.5,5.657,0.10),circle(2.5,5.657,0.12),circle(2.5,5.657,0.14),
circle(3,8,0.08),circle(3,8,0.10),circle(3,8,0.12),circle(3,8,0.14)

)}}}


<h4>Graph:</h4>

Now draw a curve through all of the points to graph {{{y=2^x}}}:



{{{ drawing(500, 500, -10, 10, -10, 10,
grid(1),
graph(500, 500, -10, 10, -10, 10, 2^x),
circle(-2,0.25,0.08),circle(-2,0.25,0.10),circle(-2,0.25,0.12),circle(-2,0.25,0.14),
circle(-1.5,0.354,0.08),circle(-1.5,0.354,0.10),circle(-1.5,0.354,0.12),circle(-1.5,0.354,0.14),
circle(-1,0.5,0.08),circle(-1,0.5,0.10),circle(-1,0.5,0.12),circle(-1,0.5,0.14),
circle(-0.5,0.707,0.08),circle(-0.5,0.707,0.10),circle(-0.5,0.707,0.12),circle(-0.5,0.707,0.14),
circle(0.5,1.414,0.08),circle(0.5,1.414,0.10),circle(0.5,1.414,0.12),circle(0.5,1.414,0.14),
circle(1,2,0.08),circle(1,2,0.10),circle(1,2,0.12),circle(1,2,0.14),
circle(1.5,2.828,0.08),circle(1.5,2.828,0.10),circle(1.5,2.828,0.12),circle(1.5,2.828,0.14),
circle(2,4,0.08),circle(2,4,0.10),circle(2,4,0.12),circle(2,4,0.14),
circle(2.5,5.657,0.08),circle(2.5,5.657,0.10),circle(2.5,5.657,0.12),circle(2.5,5.657,0.14),
circle(3,8,0.08),circle(3,8,0.10),circle(3,8,0.12),circle(3,8,0.14)

)}}} Graph of {{{y=2^x}}}