the domain is whatever you choose it to be....for example in this case it could be:
1. [-1, 1]
2. R the real numbers
3. C the complex numbers
...or infinitely many other choices.
The range will depend on the domain. If you choose the domain to be R
then the range will be (3, infinity) in R
1. [-1, 1]
2. R the real numbers
3. C the complex numbers
...or infinitely many other choices.
The range will depend on the domain. If you choose the domain to be R
then the range will be (3, infinity) in R
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Domain = all values of x for which the function is "well-defined" (for each value of x, the function gives one, and only one, clear answer).
Here, the "exponential" power can have any value. If the exponent (x-2) is a negative value, e^(x-2) will be a fraction (between 0 and 1). If x = 2, then e^(x-2) becomes e^0, which is equal to 1.
So x can be anything at all (the domain is ALL numbers).
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Range = the set of all possible "output" for the function, once you have tried all the values from the domain.
The exponential will always be positive (always a number greater than 0.
Zero itself is impossible, and negative values are impossible.
In addition, whatever the exponential gives you, you add 3 to it.
Therefore, the range will only include numbers greater than +3.
Here, the "exponential" power can have any value. If the exponent (x-2) is a negative value, e^(x-2) will be a fraction (between 0 and 1). If x = 2, then e^(x-2) becomes e^0, which is equal to 1.
So x can be anything at all (the domain is ALL numbers).
---
Range = the set of all possible "output" for the function, once you have tried all the values from the domain.
The exponential will always be positive (always a number greater than 0.
Zero itself is impossible, and negative values are impossible.
In addition, whatever the exponential gives you, you add 3 to it.
Therefore, the range will only include numbers greater than +3.