What is the domain and range of #y =2^x#?

1 Answer
Jan 7, 2018

Answer:

#color(red)("Domain" - x in RR #

#color(blue)("Range" - y > 0 #

Explanation:

Finding the domain:

We must ask what values of #x# yields a valid value of #y#, and since this is just a simple exponential function, all values of #x# gives you a real value of #y#

#color(red)("Domain" - x in RR #

Now we must consider the range, so what are the values that #y# could possiblally take on, with a sketch we can see:

graph{y = 2^x [-9.83, 10.17, -1.2, 8.8]}

We see that all possitive values of #y# can be obtained, but not #y = 0 # as this is the functions asymptotoe, and occurs as #x to oo#

#color(blue)("Range" - y > 0 #