Question 85733
x -2 -1 0 1 2
y .111 .333 1 3 9
Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, 
:
This looks like an exponential equation: y = 3^x, notice when you have
 an exponent x = 1; y = 3, that's the main clue, and when x = 2 (3^2) y = 9, Negative exponents would give very small values, positive exponents give large values in exponential equations
:
{{{ graph( 300, 200, -4, 4, -5, 50, 3^x) }}}
and give the domain and range as shown in the graph, and also the domain and range of the entire function.

The domain would be all real numbers, however y will never go to 0 or below so
the range would be all positive real numbers greater than 0
:
Prove this to yourself, make a table for the graph, Use a calculator
 x | y
-------
-4| .01236;  y = 3^-4
-3| .03704;  y = 3^-3
-2| .11111;  y = 3^-2
-1| .33333;  y = 3^-1
 0| 1; remember any number ^0 is 1
+1| 3: any number ^1 is the number
+2| 9: y = 3^2
+3| 27; y = 3^3
+4| 81; y = 3^4
:
Note that y approaches 0 but never reaches it, but no limit on it's positive value

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