# Find the Domain and Range f(x)=9-x^2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
Locate the vertex of the parabola.
Rewrite the equation in vertex form.
Reorder and .
Complete the square for .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
Cancel the common factor of and .
Factor out of .
Move the negative one from the denominator of .
Simplify the expression.
Rewrite as .
Multiply by .
Find the value of using the formula .
Simplify each term.
Raising to any positive power yields .
Multiply by .
Divide by .
Multiply by .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Use the vertex form, , to determine the values of , , and .
Since the value of is negative, the parabola opens down.
Opens Down
Find the vertex .
The range of a parabola that opens down starts at its vertex and extends to negative infinity.
Interval Notation:
Set-Builder Notation:
Determine the domain and range.
Domain:
Range:
Find the Domain and Range f(x)=9-x^2