What is the domain and range for #g(x)= x^2 - 3x#?

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Answer 1 · 2015-06-05T19:50:34

#g(x)# is well defined for all #x in RR# so its domain is #RR# or #(-oo, oo)# in interval notation.

#g(x) = x(x-3) = (x-0)(x-3)# is zero when #x = 0# and #x = 3#.

The vertex of this parabola will be at the average of these two #x# coordinates, #x=3/2#...

#g(3/2) = (3/2)^2-3(3/2) = 9/4-9/2 = -9/4#

As #x -> +-oo# we have #g(x)->oo#.

So the range of #g(x)# is #[-9/4,oo)#

graph{x^2-3x [-10, 10, -5, 5]}