Correct answers only ! which graph represents the function g(x) = 2/x-1 - 3?

D

Step-by-step explanation:

The vertical asymptote is the restriction on the x-value.  Since the denominator cannot be equal to zero, then x - 1 ≠ 0 →  x ≠ 1.     So, the vertical asymptote is: x = 1  

The horizontal asymptote is the restriction on the y-value.  Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.  However, there is a vertical shift of 3 units down so the horizontal asymptote is: y = -3

The only graph that has these asymptotes is the last one, which I call graph D.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

b and c

step-by-step explanation: