Explanation:
what was stopping you ? you started definitely correctly.
but then you began to lose concentration about the right form of brackets (vs. parenthesis). and then you did not continue.
so, let's get through it.
remember, the domain is the interval or set of all valid x- values. the range is the interval or set of all valid y-values.
and a full dot means that point is included in the interval or set (and we use "[" or "]"), an empty dot (cycle with a white belly) means the point is NOT included (and we use "(" OR ")").
"infinity" is a concept and not a value, so this is never included in an interval.
5.
domain = [-6, 2) + [3, infinity)
range = [4, infinity) + [-4, -1]
for one point -4 is excluded,
but for another it is included. so, included.
increasing = [3, infinity) + [-6, -2]
decreasing = [-2, 2)
positive = [3, infinity)
negative = [-6, 2)
6.
domain = (-9, infinity)
range = [-7, infinity)
increasing = (-9, -4] + [3, infinity)
decreasing = [-4, 3]
positive = (-9, 0] + [5, infinity)
negative = (0, 5)
as y = 0 is not negative, we have to exclude
the interception points on the x-axis.
7.
domain = [-5, 8)
range = [0, 5]
5 is excluded for one point, but included
for many other points. so, included.
increasing = [-3, 2]
decreasing = [-5, -3]
positive = [-5, 8)
negative = ()
8.
domain = (-infinity, infinity)
range = (-5, infinity)
-5 is the asymptote, the limit that will never
be reached (only in infinity). so, -5 not included
increasing = (-infinity, infinity)
decreasing = ()
positive = [4.5, infinity)
negative = (-infinity, 4.5)
again, at x = 4.5 we get y = 0, which is NOT
negative, so, 4.5 has to be excluded here.
9.
the picture is cut off, so, I cannot see the the coordinates of the bottom vertex. I assume based on your given answers that the x-coordinate is 3. and based on the visible slopes of the lines I assume the y-coordinate is -5.
but what I definitely don't know is, if there are any points excluded (like this vertex). so, I assume they are all included.
if this is not true, please adapt the brackets accordingly.
domain = (-infinity, infinity)
range = [-5, infinity)
increasing = [3, infinity)
decreasing = (-infinity, 3]
positive = (-infinity, -2] + [8, infinity)
negative = (-2, 8)