To check for continuity at the edges of each piece, you need to consider the limit as
approaches the edges. For example,

has two pieces,
and
, both of which are continuous by themselves on the provided intervals. In order for
to be continuous everywhere, we need to have

By definition of
, we have
, and the limits are


The limits match, so
is continuous.
For the others: Each of the individual pieces of
are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.
Answer:

Step-by-step explanation:
So when x and y, vary inversely, it means that the product of x and y will remain constant such that:
. This means that the function can be defined as
by dividing both sides by x. In this case x=12, and y=8, this means the constant is equal to 12 * 8 which is 96. So we have the equation:
, which can be defined as 
Answer:
Ues
Step-by-step explanation:
Ues papa math or demos and that should help
Answer:
D.
Step-by-step explanation:
The equation given takes the point-slope form which is,
. Where,
(a, b) = (x, y) coordinates of a point on the line.
m = slope of the line .
To find which graph has a line equation of
, look for the points which will give you something almost exactly as the equation if you substitute their values into
.
Let's consider option D.
We have a given point (1, 2). a = 1, b = 2.
Substitute these into 
We have:


As you can see, this looks almost exactly as
.
If you want to be certain that option D is the answer, find m by using the coordinates of any other point on the line and plug into
to find m:
In graph D, let's take the points (0, -1)
Divide both sides by -1
3 = m
m = 3.
Therefore, option D is the graph of the line
.