Question

state the domain and range of the function 2e^(x+3) + 7 in interval notation

please show work

Answer 1

domain- all real numbers.

range: (7, infinity)

Answer 2

how did you get the answer

Answer 3

For the range, look at the smallest number 2e^(x+3) + 7 can take on.

since 2e^(x+3) will always be larger than 0, 2e^(x+3) + 7 will always larger than 7. Note that since 2e^(x+3) can't be 0, seven is NOT included.

2e^(x+3) + 7 can take on infinitely large values.

Therefore the range is (7, infinity)

Also, for the domain, x can take on any value, therefore the domain is all numbers.