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

Answer 1

Kennedy Adams

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) [-0.676, 4.254, 7.593, -2.27]}

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Answer 2

Eva Adamson

To find the domain and range of ( y = 5\sqrt{(-x + 3)^4} ):

Domain: ( x \leq 3 ) Range: ( y \geq 0 )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.