<h3>
Short Answer: Yes, the horizontal shift is represented by the vertical asymptote</h3>
A bit of further explanation:
The parent function is y = 1/x which is a hyperbola that has a vertical asymptote overlapping the y axis perfectly. Its vertical asymptote is x = 0 as we cannot divide by zero. If x = 0 then 1/0 is undefined.
Shifting the function h units to the right (h is some positive number), then we end up with 1/(x-h) and we see that x = h leads to the denominator being zero. So the vertical asymptote is x = h
For example, if we shifted the parent function 2 units to the right then we have 1/x turn into 1/(x-2). The vertical asymptote goes from x = 0 to x = 2. This shows how the vertical asymptote is very closely related to the horizontal shifting.
Answer:
x= -2
Step-by-step explanation:
If you are asking for the subtraction of the equations, then I have given the correct answer. If this is not what you are looking for, please state clearly what you are looking for and I will be happy to help!!
Answer:
Step-by-step explanation:
This is a homogeneous linear equation. So, assume a solution will be proportional to:
Now, substitute 
into the differential equation:
Using the characteristic equation:
Factor out 
Where:
Therefore the zeros must come from the polynomial:
Solving for 
:
These roots give the next solutions:
Where 
and 
are arbitrary constants. Now, the general solution is the sum of the previous solutions:
Using Euler's identity:
Redefine:
Since these are arbitrary constants
Now, let's find its derivative in order to find and
Evaluating 
:
Evaluating 
:
Finally, the solution is given by:
Answer:
x > 2
Step-by-step explanation:
-2x > -4 you get this by subtracting 8 from the left side and in turn subtracting 8 from the other side
x > 2 you get this by dividing -2 from both sides
Answer:
The answer is: 9
Step-by-step explanation:
