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

1 Answer
Mar 2, 2018

Answer:

Domain: #(-oo,oo)# Range: #(0,oo)#

Explanation:

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, #(-oo,oo)#.

The range, unless the function is reflected across the #x#-axis by placing a negative sign in front of #e^x,# is #(0,oo).# 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,oo).# The #5# has no impact on the range whatsoever.