Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 1

x intercepts at x = 4 and x = -5

y intercept at 5

y=

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Dointe occible. 1

Step-by-step explanation:

Let the fractional form of the function is

As there are two vertical asymptotes at x = -4 and x = 1

so, the denominator of the function must be 0 at x=-4 as well as x=1, so, (x+4) and (x-1) is factors of the denominator, D.

D=a(x+4)(x-1)

where a is constant.

As, at x intercepts at x = 4 and x = -5, so the function is zero at x=4 and x=-5.

So, (x-4) and (x+5) are the factors of numerator, so

N=b(x-4)(x+5), where b is a constant.

From the equation (i),

As y intercept is 5, so at x=0,

f(x=0)=5

Put the value of in equation (ii), the required rational function is