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]}

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