Question 31139
x ______-2______-1______0_______1_______2
y ______.25______.5 _____1_______2_______4


Don't feel bad. It took me a little while, too. I probably tried some 
things you thought of like, is it y = 2x? No, because when x is 0
how can y = 1? The minus signs really threw me, too.

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

Then a dim light flickered. . . exponents, logs, something about negative
exponents
So I tried y = 2^x
bingo!

x_______-2______-1______0_______1_______2
2^x_____.25______.5______1_______2_______4

{{{2^(-2) = 1/4}}}
{{{2^(-1) = 1/2}}}
{{{2^0 = 1}}}
{{{2^1 = 2}}}
{{{2^2 = 4}}}

Remember, the rule for negative exponents is
{{{a^(-b) = 1/ a^b}}}
This is an exponential equation. y changes exponentially with x
---------------------------
OK, I want to graph this thing from (-2, .25) to (2,4)
(these are the (x,y) points at the ends of the chart
----------------------------
{{{ graph( 200, 200, -2, +3, -3, 6, 2^x) }}}
the domain of the data given would be it's extent on the x-axis
That would be -2 to +2
The range is the extent on the y-axis
That would be .25 to 4
------------------------------
What's the domain and range of the entire function?
That means how far can x and y possibly go?
I can make x any number I want, no problem, 
So the domain is minus infinity to plus infinity
But what happens to y (2^x) when I do this?
Y goes from a very, very small positive number to infinity
2^x can never be negative
So the  range of the entire function is zero to plus infinity