Create a rational function with known vertical and slant

Question

How can I create a rational function $g(x)$ with these requirements:

• The vertical asymptotes are at 2 and 5
• The function has a slant asymptote $y = 2x+1$
• The y-intercept is 7

Answer 1

In order to fulfill the condition on the asymptotes we can set

$$f(x)=\frac{A}{(x-2)(x-5)}+2x+1$$

and by the condition $f(0)=7$ find out A, that is A=60, thus

$$f(x)=\frac{60}{(x-2)(x-5)}+2x+1$$

Plot of f(x)