A friend believes that a 'question' he has set is solvable, but I'm arguing that it is in not in any way. He won't give me the answer or more information, but I was hoping for a second opinion. This is the exact wording that he gave me:
A function of the form $$f(x) = \tan \left(\frac{a \pi x}{b} \right) + c$$ has consecutive asymptotes at $x=-1.5$ and $x=-0.7$ and passes through the point $(-3,3.5)$. Find the values of $a$, $b$ and $c$.
What do you reckon? I'd love it if you could show the answer
My argument is that if there is no horizontal translation, then the point where x=0 has to be exactly half way in between 2 asymptotes. However, he has stated that .1.5 and -0.7 are consecutive asymptotes, and thus the period of the function has to be 0.8. If we take this to be true, then 0 is not half way between the two asymptotes: -0.7 and 0.1. That's my reasoning for the question, that you need a horizontal translation.
Problem proved to be unsolvable, thanks to aid from Blue, Fimpellizieri and theyaoster. Thanks guys!
As to why, My argument is that if there is no horizontal translation, then the point where x=0 has to be exactly half way in between 2 asymptotes. However, he has stated that .1.5 and -0.7 are consecutive asymptotes, and thus the period of the function has to be 0.8. If we take this to be true, then 0 is not half way between the two asymptotes: -0.7 and 0.1. That's my reasoning for the question, that you need a horizontal translation.