Question

write an equation for a function that has vertical asymptotes at x=3 & x=-10

Answer 1

Answer:

$\frac{5}{ {x}^{2} + 7x - 30}$

Step-by-step explanation:

We can write a rational function.

We need to make sure our denominator both have zeroes at 3 and 10.

Set an equation equal to zero to find the function

$0 - x = 3$

$0 - x = - 10$

$0 - ( - 3) = = 3$

$0 - 10 = 10$

So we would represent that's as

$x - 3$

and

$x + 10$

Multiply the two binomial together.

$(x - 3)(x + 10) = {x}^{2} + 7x - 30$

Let our numbetator be any interger.

Use any equation as long as the quadratic is the denominator and the interger is the numerator.

$\frac{5}{ {x}^{2} + 7x - 30 }$