If a function is given as $|3x - x^2|$ with range $x\le 3$, how will I find the range for the graphs for $3x-x^2$ and $-(3x-x^2)$ ?
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range $x\leq3$ or $|3x-x^2|<3$.? – Nosrati Jan 24 '17 at 11:59
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x less that or equal to 3 – warman Jan 24 '17 at 15:13
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Differentiate 3x-x^2 which is a downward facing parabola. You get 2x=3 or x=3/2. At x=3/2 the function is greatest so it's range is y<=9/4
Shashaank
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$y=3x-x^2$ is a parabola, concave, with a maximum in $x=\dfrac32$. This function cuts the $x$-axis in $x=0$ and $x=3$, so when we get absolute $|3x-x^2|$ of it, two downward branches of it turn upward. The minimum of $|3x-x^2|$ occur in $x=0$ that is $0$ and left branch of it goes $+\infty$, thus the range of it is $[0,\infty)$. For graph of this function see WolframAlpha
Nosrati
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$$3x-x^2=x(3-x)$$
$$|x(3-x)|= \begin{cases}+x(3-x) &\mbox{if }x(3-x)\ge0\iff x(x-3)\le0\iff0\le x\le3 \\-x(3-x)& \mbox{otherwise } \end{cases}$$
lab bhattacharjee
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what does 'otherwise' in this context mean? I'm sorry, I hope you'll bear with my elementary questions – warman Jan 26 '17 at 13:27