How do you determine the domain and range of y = -x^2 + 3

Question

If anyone would be willing to explain how to do it, I'd appreciate it very much!

Answer 1

y = -x² + 3

 

The domain is all possible input values of x.

There are no restrictions on what can be put in for x so the domain is

all real numbers or d = (-∞, ∞)

 

The range is all possible output values of y

 

y = -x² + 3

 

This graphs as a parabola opening downward.  The maximum output/range value will be

the y value at the vertex.  From there if will fall toward negative infinity as x

gets larger in either the positive or negative side.

 

y = -x² + 3 or f(x) = -x² + 3

 

From quadratic equation using y = ax² + bx + c we have:  a=-1, b=0, c=3

The vertex is at (-b/2a, f(-b/2a))

 

-b/2a = 0/(-2) = 0

f(0) = -(0²) + 3

f(0) = 3

 

The vertex is at (0, 3) so the range is  r = (-∞, 3]