Question

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

Answer 1

`\frac{5}{ {x}^(2) + 7x - 30}`

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 }`