How do you find the domain and range of #y = 10-x^2#?

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Answer 1 · 2017-03-05T12:01:58

Domain: #(-oo, +oo)# Range: #(-oo, 10]#

#y=10-x^2#

#y# is defined #forall x in RR#

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

#y# is a parabola with a maximum value where #y' = 0#

#y' = -2x =0 -> x=0#

#y_max = y(0) = 10#

#y# has no finite lower limit.

Hence, the range of #y# is #(-oo, 10]#

This can be inferred by the graph of #y# below:

graph{10-x^2 [-20.58, 19.95, -6.47, 13.79]}