I have a couple questions about plotting a curve with assymptotic limits.

 

1) Suppose you had the equation y = x^2. The domain for x is [-infinity, +infinity]. Therefore, there is no vertical assymptote. How would you have to modify the equation such that there is an vertical asymptote? Would it have to be a totally different equation? Obviously, it needs to be an exponentially increasing/decreasing curve (let's stick with increasing though).

 

2) Supposing you did modify the equation such that there was a vertical asymptote. What would you have to do to adjust where along the x-axis this asymptote intersected?

1.I would think that assymptotes are formed where there are no values of y which can be produced when x is a certain number. A very common assymptote is 1/x where y cannot be found when x=0.

 

This is, probably, how you would need to modify the equation.

 

2.As for your second question, I really don't understand what you mean by "What would you have to do to adjust where along the x-axis this asymptote intersected?", especially the 'intersected' part.

 

Hope this helps!

What I mean is... take the equation y = 1/x that you mentioned. The asymptote for this is at x=0. What would the equation look like if the asymptote was at x=1?

 

At this point, I can answer my own question: in order for the denominator to be 0 and x be 1, the equation would have to be y = 1/(x-1).

 

Thank you.

You kind of solved the problem yourself. Vertical asymptotes will always appear when you have a fraction and certain values of x for which the denominator becomes 0 while the nominator doesn't.

 

So a (simple) function of the form y = 1/(x-a) will always yield a vertical asymptote at x = a.

 

Just substitute a to get a vertical asymptote at any desired x-value.

Please allow me to add to that:

f(x)= the normal function

f(x+a)= is a shift in the left direction (ie the graph moves towards the leftof the graph) It works the opposite of what you might think

f(x)+a= the graph moves upwards, exactly what you might think