How do you find the domain and range of g(x) = 5e^x

musicbachv7

musicbachv7

Answered question

2022-08-11

How do you find the domain and range of g ( x ) = 5 e x ?

Answer & Explanation

Payton Mcbride

Payton Mcbride

Beginner2022-08-12Added 18 answers

By default, the domain of the natural exponential function, or the values of x for which f ( x ) = e x exists, is all real numbers, ( , )
The range, unless the function is reflected across the x-axis by placing a negative sign in front of e x , is ( 0 , ). This is because e x can never equal zero (hence the open interval) and can never be negative -- these are fundamental properties of the exponential function. Furthermore, e x increases as we plug in larger and larger values of x, it goes to infinity.
Here, our function involves no negative signs; thus, our range is ( 0 , ). The 5 has no impact on the range whatsoever.

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