Correct answers only ! what are the equations for the vertical and horizontal asymptotes of the function?

(A) vertical asymptote: x = 2, horizontal asymptote: y = 1

Step-by-step explanation:

Vertical Asymptote is the restriction on the x-value.  The denominator cannot be zero, so x - 2 ≠ 0  ⇒  x ≠ 2

The restricted value on x is when x = 2  which is the vertical asymptote

Horizontal Asymptote (H.A.) is the restriction on the y-value.  This is a comparison of the numerator (n) and denominator (m).  There are 3 rules that will help you:

In the given problem, n < m so y = 0, however there is also a vertical shift of up 1 so the H.A. also shifts up.  This results in H.A. of y = 1

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: