can you help with radical + rational functions?

Question

Find an expression for a rational function ƒ(x) that satisfies the conditions: a slant asymptote at y = 100x, vertical asymptote at x = −50, and contains the point (0, 0).

Answer 1

Vertical asympotote x  = -50, slant asymptote y  = 100x and contains point (0,0).

To get vertical asymptote write the equation like f (x ) = a / (x + 50) , numerator 'a' need to find out.

For the slant asymptote 100x  add it to the equation.

now the quation becomes

f(x) = 100x + a / (x + 50)

Plugin the values (0,0) to solve for a

0 = 100x + a / (x + 50)

0 = 100(0) + a / (0 + 50)

0 =  a / 50

a = 0

Now the final equation is  f(x) = 100x - (0 / (x + 50))

The rational function is f (x ) = (100x ^2 + 5000x )/(x + 50) .

 

Comments

I think the final equation is  f(x) = 100x