How do you find the domain and range of #y= 5sqrt((-x+3)^4)#?

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Answer 1 · 2017-11-04T07:48:29

Donain: #(-oo,+oo)# Range: #[0, +oo)#

#y= 5sqrt((-x+3)^4) #

#= 5xx (-x+3)^(4/2) = 5(-x+3)^2#

#y# is defined #forall x in RR#

Hence, the domain of #y# is: #(-oo,+oo)#

#y_min = y(3) = 0#

#y# has no finite uper bound.

Hence, the range of #y# is: #[0, +oo)#

As can be deduced from the graph of #y# below.

graph{5sqrt((-x+3)^4) [-2.27, 7.593, -0.676, 4.254]}