Transformations: Let f(x)=a(x-p)^2+q be a quadratic function, where....

[Alitlestarlight]

Let f(x)=a(x-p)^2+q be a quadratic function, where a,p,q are constants and a is not equal to zero. F(x) is translated up by k units, translated right by c units, and then take a reciprocal of the translated function. Define g(x) be the function after performing all the transformations.

A. Find the conditions on the constants a, q, and k so that g(x) does not have a vertical asymptote.
B. Find the x values so there are invariant points linking f(x) and 1/f(x)

I'm not even sure where to start on this question. I know that for there to be no vertical asymptotes if the denominator is zero. But I'm not sure how to go about figuring this out. Even just a little start would be nice! Thank you!

 

[Deleted member 4993]

Let f(x)=a(x-p)^2+q be a quadratic function, where a,p,q are constants and a is not equal to zero. F(x) is translated up by k units, translated right by c units, and then take a reciprocal of the translated function. Define g(x) be the function after performing all the transformations.

A. Find the conditions on the constants a, q, and k so that g(x) does not have a vertical asymptote.
B. Find the x values so there are invariant points linking f(x) and 1/f(x)

I'm not even sure where to start on this question. I know that for there to be no vertical asymptotes if the denominator is zero. But I'm not sure how to go about figuring this out. Even just a little start would be nice! Thank you!

What are the differences between f(x) and F(x) ?

 

[Dr.Peterson]

Let f(x)=a(x-p)^2+q be a quadratic function, where a,p,q are constants and a is not equal to zero. F(x) is translated up by k units, translated right by c units, and then take a reciprocal of the translated function. Define g(x) be the function after performing all the transformations.

A. Find the conditions on the constants a, q, and k so that g(x) does not have a vertical asymptote.
B. Find the x values so there are invariant points linking f(x) and 1/f(x)

I'm not even sure where to start on this question. I know that for there to be no vertical asymptotes if the denominator is zero. But I'm not sure how to go about figuring this out. Even just a little start would be nice! Thank you!

I'll assume that f was just accidentally capitalized in the one place.

Have you written an equation for g(x)? That will be the first step. Then you can look at the and find the conditions under which the denominator will never be zero.