Do you know the domain or the range of y = ex ?nukeman said:Homework Statement
Determine the domain and range of the function y=5−e^(−x/2).
I am having some trouble with this. Does any have some tips to get started, or a good link to a instructional video? My textbook does not have this section :(
Thanks all!
Homework Equations
The Attempt at a Solution
So, you have no experience with exponential functions.nukeman said:Thats a negative.
I just got to the "e" now, but my book does not explain this. So, that's why I am asking here.
The domain of the function y=5−e^(−x/2) is all real numbers, since there are no restrictions or limitations on the values that x can take.
Yes, the function is defined for all real numbers since there are no restrictions on the values that x can take.
The range of the function y=5−e^(−x/2) is all real numbers greater than or equal to 5. This is because the exponential term e^(−x/2) will always be positive, and subtracting it from 5 will result in a value that is always greater than or equal to 5.
To determine the domain and range algebraically, you can use the general rules for finding the domain and range of exponential functions. The domain of any exponential function is all real numbers, and the range is all positive numbers. Then, by subtracting the exponential term from 5, we can see that the range of this specific function is all real numbers greater than or equal to 5.
No, there are no values that the function y=5−e^(−x/2) cannot take. As mentioned before, the domain of this function is all real numbers, so there are no restrictions on the values that x can take. Additionally, since the exponential term e^(−x/2) is always positive, there are no limitations on the resulting values of the function.