Question 6 select the system of linear inequalities whose solution is graphed. x ≤ –2; y ≤ –x – 3 x < –3; y < –x – 2 x < –2; y ≤ –x + 2 x < –2; y ≤ –x – 2

The correct answer is x ≠ -2, y ≤ -x - 2.

No shaded half-plane from the line x = -2 (right: x> -2 or left x <-2)

A bit of further explanation:

The parent function is y = 1/x which is a hyperbola that has a vertical asymptote overlapping the y axis perfectly. Its vertical asymptote is x = 0 as we cannot divide by zero. If x = 0 then 1/0 is undefined.

Shifting the function h units to the right (h is some positive number), then we end up with 1/(x-h) and we see that x = h leads to the denominator being zero. So the vertical asymptote is x = h

For example, if we shifted the parent function 2 units to the right then we have 1/x turn into 1/(x-2). The vertical asymptote goes from x = 0 to x = 2. This shows how the vertical asymptote is very closely related to the horizontal shifting.