Question

Write an equation for a rational function with the given characteristics. Vertical asymptotes at x = -1 and x = 3, x-intercepts at (-5,0) and (2,0), horizontal asymptote at y= 1 Enclose numerators and denominators in parentheses. For example, (a - b)/(1+ n). f (x) =

Answer 1

Given:

Vertical asymptotes at x = -1 and x = 3

X- intercept = (-5, 0 ) and ( 2 , 0 )

And horizontal asymptote at y= -6

So,

The equation has two zeros at x = -5 , and x = 2

So, there are two factors: ( x + 5 ) and ( x - 2 )

The zeros are calculated when f(x) = 0

So, the numerator = ( x + 5 ) * ( x - 2 )

By the vertical asymptotes , we will find the zeros of the denominator

So, the zeros of the denominator are: x = -1 and x = 3

So, the factors are : ( x + 1 ) and ( x - 3 )

So, the denominator = ( x + 1 ) * ( x - 3 )

So, the function will be:

`((x-2)(x+5))/((x-3)(x+1))`