Question

Use a given information to create the equation for the rational function. The function is written in factored form to help you see how the given information shapes our equation. Enter the values for factor from smallest to largest.

Answer 1

we have that

the numerator is

a(x-1)(x-5)

where a is the leading coefficient of the numerator

the denominator is

(x+4)(x+1)

so

$f(x)=\frac{a\mleft(x-1\mright)\mleft(x-5\mright)}{\mleft(x+4\mright)\mleft(x+1\mright)}$

Find out the value of a

the y-intercept is (0,7)

substitute

$7=\frac{a(0-1)(0-5)}{(0+4)(0+1)}$$7=\frac{a(-1)(-5)}{(4)(1)}$$\begin{gathered} 7=\frac{5a}{4} \\ a=\frac{28}{5} \end{gathered}$

therefore

the numerator is (28/5)(x-1)(x-5)

and

the denominator is (x+4)(x+1)