Question 84133
Using the table we have, lets plot these points

<pre>
<TABLE width=500>

<TR><TD> x</TD><TD>y</TD></TR>

<TR><TD> -2</TD><TD>.25</TD></TR> 
<TR><TD> -1</TD><TD>0.5</TD></TR> 
<TR><TD> 0</TD><TD>1</TD></TR> 
<TR><TD> 1</TD><TD>2</TD></TR> 
<TR><TD> 2</TD><TD>4</TD></TR> 
<TR><TD> </TD><TD></TD></TR> 
</TABLE>
</pre>

Plot the 1st point (-2,.25)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,.25,0.05),
  circle(-2,.25,0.08)
  )}}}


Plot the 2nd point (-1,0.5)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,.25,0.05),
  circle(-2,.25,0.08),circle(-1,0.5,0.05),
  circle(-1,0.5,0.08)
  )}}}


Plot the 3rd point (0,1)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,.25,0.05),
  circle(-2,.25,0.08),circle(-1,0.5,0.05),
  circle(-1,0.5,0.08),circle(0,1,0.05),
  circle(0,1,0.08)
  )}}}


Plot the 4th point (1,2)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,.25,0.05),
  circle(-2,.25,0.08),circle(-1,0.5,0.05),
  circle(-1,0.5,0.08),circle(0,1,0.05),
  circle(0,1,0.08),circle(1,2,0.05),
  circle(1,2,0.08)
  )}}}


Plot the 5th point (2,4)

{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,.25,0.05),
  circle(-2,.25,0.08),circle(-1,0.5,0.05),
  circle(-1,0.5,0.08),circle(0,1,0.05),
  circle(0,1,0.08),circle(1,2,0.05),
  circle(1,2,0.08),circle(2,4,0.05),
  circle(2,4,0.08)
  )}}}

By drawing a line through the points, we get 


{{{drawing( 700, 700, -10, 10, -10, 10,
  grid( 1 ),circle(-2,.25,0.05),
  circle(-2,.25,0.08),circle(-1,0.5,0.05),
  circle(-1,0.5,0.08),circle(0,1,0.05),
  circle(0,1,0.08),circle(1,2,0.05),
  circle(1,2,0.08),circle(2,4,0.05),
  circle(2,4,0.08),graph( 700, 700, -10, 10, -10, 10, 2^x) 
  )}}}


So by now you can see that the graph is a curve in which is growing at an exponential rate. So the graph of the function is exponential. The domain is the set of x values which will produce a y value. Since any x will work, the domain is all real numbers. The range is the set of y values that come out. So the range is {{{y>0}}} since the graph doesn't go below the x axis