How do you graph #f(x)=4^(x-2)# and state the domain and range?

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Answer 1 · 2017-08-31T17:17:36

domain is #{ x in RR }#
range is #{ y in RR^+ : y != 0 }#

#f(x) = 4^(x-2)# is a continuous function for all #RR#
So domain is #{ x in RR }#

#4^(x-2)# can never equal 0.

If #x >= 2# then # 4^(x-2) >= 1 #

If #x < 2 # then #4^(x - 2)# #= 1/(4^(2 - x)#

As #x -> -oo# then #1/(4^(2 - x)) -> 0#

So range is #{ y in RR^+ : y != 0 }#

#y# axis intercept is #1/16# where #x = 0#

The #x# axis is a horizontal asymptote.

graph{y = 4^(x - 2) [-8.89, 8.885, -4.444, 4.44]}