Give the domain and range of the relation, and state whether or not it is a function: { (-3,10), (-3, 16), (11, 30)}

Question

Give the domain and range of the relation, and state whether or not it is a function:

{ (-3,10), (-3, 16), (11, 30)}

I am not entirely sure how to do this. Pls help....

Answer 1

It's not a function because there are 2 y values for 1 x value. when x=-3 there is no unique y value

It looks like a rightward opening parabola. range would be any real number. domain would be x> a negative number, maybe about -100 or -200 or so

axis of symmetry is y = average of 10 and 16 = 13, the vertex is (x,13)

a 4th point on the parabola is (11, -4) symmetric with (11,30) about y=13

find the vertex x coordinate and that would give the minimum value for the domain.

the directrix will be x= the minimum value in the domain

general form of the parabola in vertex form is

x = a(y-k)^2 + h where (h,k) is the vertex and h is the minimum point of the domain and k= 13

plug in two points and solve for h and a

11 = a(30-13)^2 + h = 289a + h

plug in another point

-3 = a(10-13)^2 + h = 9a + h

subtract 2nd from 1st to get

14 = 280a

a = 280/14 = 20

x = 20(y-13)^2 + h

-3 = 20(10-13)^2 + h

h = -183, the vertex is (-183,13)

the domain is x> -183