What is the domain and range of #f(x) = 3+sqrt(x-21)#?

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Answer 1 · 2017-07-04T03:15:35

See below.

We can determine the domain and range of this function by comparing it to the parent function, #g(x)=sqrt(x)#.

In comparison to the parent function, #f(x)# is a vertical shift #3# units upward and a horizontal shift #21# units to the right.

Based on this, we also know that the domain and range must have also changed this much from the parent function.

Therefore, if we look at a graph of the parent function #g(x)#, we can write the following domain and range:

#"Domain": x>=0#
#"Range": y>=0#

After applying the transformations, we get:

#"Domain": x>=21#
#"Range": y>=3#

I hope that helps!