can you help with rational and radical functions, please?

Question

Find an expression for a rational function f(x) that satisfies the conditions: a slant asymptote of y = 2x, vertical asymptote at x = 1, and contains the point (0, 6).

Answer 1

To get vertical asymptote write the equation like f(x) = a / (x - 1) , numerator 'a' need to find out.

For the slant asymptote 2x add it to the equation.

now the quation becomes

f(x) = 2x + a / (x - 1)

Plugin the values to solve for a

6 = 2x + a / (x - 1)

6 = 2(0) + a / (0 - 1)

6 =  a / -1

a = - 6

Now the final equation is  f(x) = 2x - (6 / (x - 1))

f(x) = (2x^2 - 2x - 6)  / (x - 1)