What is the oblique asymptote of the function f(x) = the quantity x squared plus 5x plus 6 over the quantity x minus 4? y = x + 9 y = x − 9 y = x + 1 y = x − 1

Answer y = x+9

Given function f(x) =

To find out oblique asymptote we use long division

We divide x^2 + 5x + 6 by x-4

Hereby attached a file that shows long division

Long division steps are given below

1. Divide the first term of both numerator by denominator (x^2/x = x)

2. Multiply the answer x with x-4 that gives x^2 - 4x and put it at the bottom

3. Change the sign and subtract it

4. Repeat the step 1,2,3 till we get the remainder

We got quotient is x+9

So we write oblique asymptote y = x+9

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:

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step-by-step explanation: