Question

Can someone please help me with these questions and explain I'm so confused :( You have to make a function

A polynomial with rational coefficients having roots 3, 3, and 3-i

A rational function with vertical asymptote and horizontal asymptote

Answer 1

A polynomial with rational coefficients having roots 3, 3, and 3-i
That means tha plugging in those values for x will make the function 0.
Also, if 3 - i is a zero...3 + i must also be a zero.
In other words f(x) = (x - 3)(x - 3)(x - (3 - i))(x - (3 + i))
Simplifying that, which is a pain but very quick using the EXPAND command at wolframalpha .com...that simplifies to 90-114 x+55 x^2-12 x^3+x^4

Answer 2

A rational function with vertical asymptote and horizontal asymptote

You want to make sure that your denominator = 0 for some value of x AND
that the degree of your numerator is the same as the degree of your denominator.
Example