How do you find the domain and range of $y = 4x - x ^2$ ?

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Answer 1 · 2017-03-01T12:29:26

Domain: $(-oo, +oo)$
Range: $(-oo, 4]$

$y= 4x-x^2$

$y$ is defined $forall x in RR$
Hence the domain of $y$ is $(-oo, +oo)$

Since the coefficient of $x^2$ is -ve, y has a maximum value where $y'=0$

$y' = 4 -2x=0$

$x=2 -> y_max =4*2 - 2^2 =4$

Thus the range of $y$ is: $(-oo, 4]$

This can be observed from the graph of $y$ below.

graph{x(4-x) [-6.4, 6.087, -1.347, 4.897]}

How do you find the domain and range of y = 4x - x ^2y = 4x - x ^2?