Which of the following is the set of real numbers that are 4 units from 7?

  see below

Step-by-step explanation:

The difference of 7 and x is 7-x. The difference of x and 7 is x -7. If you want the positive difference regardless of which (7 or x) is larger, you can make the difference be positive by using the absolute value: |x -7|.

We want numbers such that this difference is 4, so we want the solutions to ...

  |x-7| = 4

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: