I need the answer to the image attached
below

y = 0

Step-by-step explanation:

Given a rational function

f(x) =

If the degree of g(x) < degree of h(x), then

y → 0 as x → ± ∞

Thus y= 0 ( the x- axis ) is the horizontal asymptote

For the given rational function

The numerator is of degree 2 while the denominator is of degree 3

Thus

y = 0 is the horizontal asymptote of r(x)

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!