How do you find the domain and range of #y = 4x - x ^2#?

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Answer 1 · 2017-03-01T12:29:26

Domain: #(-oo, +oo)#
Range: #(-oo, 4]#

#y= 4x-x^2#

#y# is defined #forall x in RR#
Hence the domain of #y# is #(-oo, +oo)#

Since the coefficient of #x^2# is -ve, y has a maximum value where #y'=0#

#y' = 4 -2x=0#

#x=2 -> y_max =4*2 - 2^2 =4#

Thus the range of #y# is: #(-oo, 4]#

This can be observed from the graph of #y# below.

graph{x(4-x) [-6.4, 6.087, -1.347, 4.897]}