Answer:
domain F(x) = All real numbers
Range F(x) [ -2 , + ∞ ]
Step-by-step explanation:
There are three points of the curve
P₁ ( -1,5 , 0 ) Q ( 0. -2 ) and P₂ ( 1,5 , 0 )
We can see that P₁ and P₂ are simmetric around y axis, and point Q looks like a vertex we conclude the curve is of the form
ax² + bx + c = y
The curve is a parabola
when x = 0 y = -2 then c = - 2
And plugging in the coordinates of the points in the equation we get:
a (-1,5)² + b (-1,5) + c = 0 ⇒ 2,25*a - 1,5*b - 2 = 0
a (1,5)² + b ( 1,5) + c = 0 ⇒ 2,25*a + 1,5*b -2 = 0
Adding these two equations
4.5*a - 4 = 0
a = 4/4,5
as vertex is Q ( 0 , -2 )
x = - b/2a ⇒ 0 = - b/ 9 ⇒ b = 0
Therefore the equation of the function is:
ax² + c = 0
(4/4,5) x² - 2 = 0
Having the equation we can determine Domain
domain F(x) = All real numbers
Range F(x) [ -2 , + ∞ ]
