What is the domain and range of #y =9 - x^2#?

1 Answer
Jacq
Sep 8, 2017

D: All real x
R: #y<=9#

Explanation:

#y = 9 - x^2# is an upside down parabola that has been shifted up 9 units. If it helps, you can rewrite the equation to make #y = -x^2 + 9#.

The domain of any parabola is all real x, or #x in RR#. This does not change when shifting the parabola.

The range of a normal parabola (#y = x^2#) is #y>=0#.

The range of an upside-down parabola (#y = -x^2#) is #y<=0#.

Shifting the parabola up by 9 just increases the range from starting at 0 to starting at 9.

So the domain and range are:
D: All real x
R: #y<=9#

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