Question 849709
Make an x_y table.

x  |  y

-2   (1/4)e^-2
-1   (1/4)e^-1
0    (1/4)
1    (1/4)e
2    (1/4)e^2

If you are not allowed to use a calculator, let's approximate what some of these values are.

The easy one is we know (0,(1/4)). That's pretty simple to plot, we can even call it (0,.25).

What about (1/4)*e?  We know that e is 2.71828, so if we were to take a 4th of it we'd get roughly .67. 

What about (1/4)*e^2 We can imagine that the square of e is going to be slightly under 9 since 2.71<3. So, I'll guesstimate and say it's 8.8. It really doesn't matter. What's important is you are close.

You can see that as we increase x, y is increasing at a much larger rate. It's going to look similar to our exponential function.

What about the other way?

(1/4)*e^-1.  Well e^-1 = 1/e  so if we treat e as 3, just to get close, we see that we'd be pretty close to 1/12 = .0833, when we actually plug in (1/4)*e^-1 we get .0919. So off a bit, but we can at least start to see the shape.

(1/4)*e^-2 = 0.034. Notice we're getting closer and closer to 0 as we approach smaller and smaller numbers. Will we ever reach 0 though? No.

When we start to put this together our graph looks like this:

<img src ="http://www4b.wolframalpha.com/Calculate/MSP/MSP58431bibde6204926c1i0000171i04cbhg263b6b?MSPStoreType=image/gif&s=8&w=300.&h=406.&cdf=Resizeable" />

Adding a little fill to this gives us a graph like this.

<img src ="http://www4b.wolframalpha.com/Calculate/MSP/MSP300521haf97d3fcaha49000048c61ie30ide1ffe?MSPStoreType=image/gif&s=30&w=300.&h=196.&cdf=RangeControl"/>