What is the range of the function #f(x)= -x^2 +9#?

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Answer 1 · 2017-09-02T13:17:18

Range of #f(x) = [9, -oo)#

#f(x) = -x^2+9#

#f(x)# is defined #forall x in RR#

Hence, the domain of #f(x) = (-oo, +oo)#

Since the coefficient of #x^2 <0# #f(x)# has maximum value.

#f_max = f(0) = 9#

Also, #f(x)# has no lower bounds.

Hence, the range of #f(x) = [9, -oo)#

We can see the range from the graph of #f(x)# below.

graph{-x^2 +9 [-28.87, 28.87, -14.43, 14.45]}