Question

Write two functions whose graphs are translations of the graph y=∜x . The first function should have a domain of x≤5. The second function should have a range of y≥-7.

Answer 1

ok original function has domain of x>0 , range y>0

you change domain by either reflecting or shifting graph left/right
you change range by either reflecting or shifting up/down

for domain to be x <5 , shift graph 5 units to the right, then reflect it
\[y = \sqrt[4]{-(x-5)}\]

for range to be y>-7 , shift graph 7 units down
\[y = \sqrt[4]{x} - 7\]

Answer 2

thanks so much!

Answer 3

yw :)