Question

Make a rational equations with the following requirements

vertical asymptote x= 5, x=-5

x intercepts (2,0) (1,0)

Y intercept (0,4)

Answer 1

`f(x)=(-50(x-1)(x-2))/((x-5)(x+5))`

Explanation:

Since f(x) has asymptotes at x = 5 and x = -5, then the denominator of the rational function contains the terms (x - 5) and (x + 5):

`f(x)=(?)/((x-5)(x+5))`

Since f(x) has x-intercepts at x = 2 and x = 1, then the numerator of the rational function contains the terms (x - 2) and (x - 1):

`f(x)=(A(x-1)(x-2))/((x-5)(x+5))`

Now substitute the point (0, 4) and solve for A:

`f(0)=4\\\\\implies (A(0-1)(0-2))/((0-5)(0+5))=4\\\\\\\implies -(2)/(25)A=4\\\\\\\implies A=-50`

So final rational function:

`f(x)=(-50(x-1)(x-2))/((x-5)(x+5))`