x	-2	-1	0	1	2
y	.111	.333	1	3	9

Given the table above, plot the five given points:



Now draw a smooth curve through the five points:



identify the graph of the function (line, parabola, hyperbola, or 
exponential), explain your choice,

It is an exponential.  First of all it looks like the exponential
graphs we have studied before.  But mainly,

I observe that the last value of y is the 2nd power of 3,
     and that 2, the exponent, is the value of x.

I observe that the next to the last value of y is the 1st power of 3,
     and that 1, the exponent, is the value of x.

I observe that the middle value of y is the 0 power of 3,
     and 0, the exponent, is the value of x.

So I suspect that each y value equals the xth power of 3.

If I am right, then .333 should be the -1 power of 3.

Let's see:   =  = .333.....

That checks out, and if I am right, then .111 should be
the -2 power of 3.

Let's see:   =  =  = .111.....

That checks out, too.  So the equation of the graph must be 

y = 

That is an exponential function, because each y-values is 
the 3 raised to the exponent of the value of x.

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

and give the domain and range as shown in the graph,

The domain in the graph is [-2,2] or {x|-2 < x < 2}

The range in the graph is [.111,9) or {y|.111 < y  9}

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and also the domain and range of the entire function

The domain of the entire function is (-oo,oo) as the
values of x go on indefinitely in both directions.

The range is (0,oo)

Edwin