Question 72923
<pre><font size = 5><b>
x  -2 -1 0 1 2
y .25 .5 1 2 4 
Given the table above, graph the function, 
identify the graph of the function (line, 
parabola, hyperbola, or exponential), 
explain your choice, and give the domain 
and range as shown in the graph, and also 
the domain and range of the entire function. 
Graph 
Graph Type 
Explanation 
Domain 
Range 

Plot those points, connect them with a smooth
curve and get this:

{{{ graph( 240, 300, -2, 2.1, -1, 4.1, 2^x) }}}

That graph looks like an exponential function, 
because an exponential function has the x-axis 
as its horizontal asymptote on the left and it 
passes through y-intercept (0,1) and "sky-rockets"
thereafter on the right.

Its domain is (-<font face = "symbol">¥</font>,<font face = "symbol">¥</font>) because the curve projects 
downward onto the entire x-axis.

Its range is (0,<font face = "symbol">¥</font>) because the entire curve 
projects right and left onto only the top half 
of the y-axis, (0,<font face = "symbol">¥</font>)

BTW its equation is y = 2<sup>x</sup>.  If you need to know
this and why, post again.

Edwin</pre>