Answer:
drawing the graph of 
The graph is attached in the images below.
Option A is correct option.
Step-by-step explanation:
We are given:
and 
We need to find graph of (fog)(x)
We know that (fog)(x)= f(g(x))
Placing x=g(x) i,e x=|x|

Now, drawing the graph of 
The graph is attached in the images below.
Option A is correct option.
The transaction that is being used is a reflection
Answer:
Step-by-step explanation:
given a point
the equation of a line with slope m that passes through the given point is
or equivalently
.
Recall that a line of the form
, the y intercept is b and the x intercept is
.
So, in our case, the y intercept is
and the x intercept is
.
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph
. Which means that 
The slope of the tangent line is given by the derivative of the function evaluated at
. Using the properties of derivatives, we get
. So evaluated at
we get 
Replacing the values in our previous findings we get that the y intercept is

The x intercept is

The triangle in consideration has height
and base
. So the area is

So regardless of the point we take on the graph, the area of the triangle is always 2.
It would be 82 2/3 since 1/3 minis 2/3 would equal -1/3 you subtract that from 83 and get 82 2/3