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

Question

10388 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-08T11:53:24

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

$y = 9 - x^2$ 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: $y<=9$

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