Question 179180
{{{x^2+y = 10}}} Start with the given equation



{{{y = 10-x^2}}} Subtract {{{x^2}}} from both sides.



Domain:


So we can see here that we can plug in <i>any</i> value for "x" and get a real number for "y". This means that the domain is all real numbers, which is *[Tex \LARGE \left(-\infty,\infty\right)] in interval notation.


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Range:

Now there are different ways about going to find the range. You could graph the equation {{{y = 10-x^2}}} to find the set of y values. It turns out that this function graphs a parabola. Since parabolas have either a min or a max, this means that either the set of y values is either less than or equal to the max OR the set of y values is greater than or equal to the min.



In this case, since the coefficient for the {{{x^2}}} term is -1, this means that the parabola will open down and that the parabola has a max. It turns out that the max value is 10. So the range is {{{y<=10}}} which in interval notation is <font size=6>(</font>*[Tex \LARGE -\infty,10]<font size=6>]</font>