Given:
The given function is:
The graph of the function is given.
To find:
The end behavior of the given function.
Solution:
We have,
From the given graph it is clear that the function approaches to -4 at x approaches negative infinite and the function approaches to negative infinite at x approaches infinite.
as
as
Therefore, the end behaviors of the given function are:
as
as
Given function is
now we need to find the value of k such that function f(x) continuous everywhere.
We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.
So we just need to find both left and right hand limits then set equal to each other to find the value of k
To find the left hand limit (LHD) we plug x=-4 into 3x+k
so LHD= 3(-4)+k
To find the Right hand limit (RHD) we plug x=-4 into
so RHD=
Now set both equal
k=-0.47
<u>Hence final answer is -0.47.</u>