How do you find the domain and range of e^(-4t)e4t?

1 Answer
Nov 21, 2017

Domain: All Reals
Range: Y>0

Explanation:

Start by finding the Domain (t values) and then use that information to solve for the Range (y values)

for e^(-4t)e4t look for the number t cannot be.

Look for things such as:
-Dividing by 0
-Taking a root of a negative number
-Taking the lnln of a negative number

e^(-4t) = 1/(e^(4t))e4t=1e4t

Now the only issue is that the denominator cannot equal 0.
But ee (being a positive number) to any power will be a number greater than 0 and so there are no exceptions for tt.

Therefore the Domain is all real numbers.

The Range would then be the results of all the values of tt.

When t is really really big the equation gets closer and closer to 0.
(1/10000000 = 0.0000001)(110000000=0.0000001) As tt gets bigger the the result gets closer and closer still to zero, but never equals zero. So its always positive as tt gets larger.

When tt is small (less than 0) you get e^-(4(-t))e(4(t)) or simply e^(4t)e4t
So as tt increases the result goes to infinity. So again we get all positive numbers.

Therefore the range is all values greater than 0.

You can also see this graphically.

graph{e^(-4x) [-10, 10, -10,10]}