How do you find the domain and range of $y = 10 - x^{2}$ $y = 10-x^2$ ?

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Answer 1 · 2017-03-05T12:01:58

Domain: $(- \infty, + \infty)$ $(-oo, +oo)$ Range: $(- \infty, 10]$ $(-oo, 10]$

$y = 10 - x^{2}$ $y=10-x^2$

$y$ $y$ is defined $forall x in RR$

$:.$ the domain of $y$ is $(-oo, +oo)$

$y$ is a parabola with a maximum value where $y' = 0$

$y' = -2x =0 -> x=0$

$y_max = y(0) = 10$

$y$ has no finite lower limit.

Hence, the range of $y$ is $(-oo, 10]$

This can be inferred by the graph of $y$ below:

graph{10-x^2 [-20.58, 19.95, -6.47, 13.79]}

How do you find the domain and range of y = 10-x^2y=10−x2y = 10-x^2?