find the vertical and horizontal asymptotes, Then write the domain and range using interval notations of the image below?

Question

image here https://ibb.co/kqjRG5B

Answer 1

VA: x = -3

HA: y = 1

Domain: (- ∞, - 3)U(-3, - 2)U(- 2,∞)

Range: (- ∞, -3)U(-3, 1)U(1,∞)

Answer 2

When you look at the image reference, the vertical and horizontal asymptotes are the dotted lines shown in blue. so, that's pretty easy

Horizontal Asy: y = 1

Vertical Asy: x = -3

Interval notation uses rounded and squared off brackets (rounded if it does not include the number, squared off if it does).

The domain is all the values allowed to put in for X. As you can see there is an asymptote at x = -3, and you also see there is a open circle at x=-2, so the domain would be (-∞,-3),(-3,2),(2,+∞) (you are looking horizontal for domain values)

The range (you look vertical, the y values that comes out of entering the x values above): you see an asymptote at y=1 and a hole at y=-3, so the range would be (-∞,-3), (-3,1), (1,+∞)

It takes a while to get used to what domain and range represent, but once you understand it, it's fairly easy to pick out the intervals. I hope this helps.