What is the domain of the following function?

Hello!

The domain is the set of all possible x-values which will make the function true, and will output real y-values.

There are 5 points graphed. (0, 0), (1, 4), (2, 1), (3, 3), and (4, 1). Ordered pairs are written as (x, y), and the x-values are the domain of this graph.

Therefore, the domain of this function is 0 ≤ x ≤ 4, [0, 4], and {x | 0 ≤ x ≤ 4}. These are just several ways to write the domain.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

the answer is 8/21

hope this