What is the domain and range of #y=-5^x# ?

What is the domain and range of #y=-5^x# ?

1 Answer
VNVDVI
Mar 2, 2018

Domain: #(-oo,oo)# Range: #(-oo,0)#

Explanation:

By default, the domain of the exponential function, or the #x# values for which it exists, is #(-oo, oo)#

The range of the parent exponential function, #y=b^x,# where #b# is the base, is #(0,oo)# because by default, the exponential function can never be negative or zero, but it keeps increasing forever.

Here, #b=-5#. The negative implies that we've flipped the graph of our function about the #x#-axis; therefore, our range will be #(-oo,0)#, because our function will never be positive (the negative sign ensures that) or zero and keeps decreasing forever due to the negative.

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