Question 849709: I do not understand how to even begin on anything like this. I asked my professor and three other students about it but they didn't help me to understand it that much at all.
Graph the function by substituting and plotting points.
y=(1/4)e^x
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! 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:
Adding a little fill to this gives us a graph like this.
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