Question

Write an equation for a rational function with:

Answer 1

Answer:

$y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}$

Step-by-step explanation:

Because x=1 and x=4 are the solutions to x-1=0 and x-4=0, then we have (x-1)(x-4) in the denominator.

Because (-1,0) and (-6,0) are the solutions to x+1=0 and x+6=0, then we have (x+1)(x+6) in the numerator.

Now we have $y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}$ where we plug in (0,8) to solve for a:

$y=\frac{a(x+1)(x+6)}{(x-1)(x-4)}$

$8=\frac{a(0+1)(0+6)}{(0-1)(0-4)}$

$8=\frac{6a}{4}$

$32=6a$

$\frac{32}{6}=a$

$\frac{16}{3}=a$

Therefore, the equation for the rational function is $y=\frac{\frac{16}{3}(x+1)(x+6)}{(x-1)(x-4)}$