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How do you find the domain and range of #f(x) = 3(1/2)^x#?

1 Answer
Dec 12, 2017

Answer:

Domain: #x in RR #
Range: # f(x) > 0 #

Explanation:

We can first sketch the function to enable us to determine the domain and range:

graph{3*(1/2)^x [-9.16, 10.84, -2.12, 7.88]}

I am assuming you are aware of how to sketch this function

Now we can consider the domain:

The fucntion is defined for all values of #x# ie, it will always output #f(x)# where #f(x)# is real, or we can write as #AA x, f(x) in RR #

#=> x in RR#

Now we can find the range:

We see that there is a asymptote at #y = 0 # we the function #f(x)# gets closer to #0# as #x-> oo # but will never touch #y=0#

But then #f(x) # can take on all the other positive real numbers:

#=> f(x) > 0 #