Question

How do you find the intercepts for `F(x)=(x^2+x-12)/(x^2-4)`?

Answer 1

x= -4 , x = 3 , y=3

Explanation:

When any function crosses the x-axis , the corresponding y-coordinate will be zero. By letting y = 0 , we can find the x-intercept.

hence : `(x^2 + x - 12)/(x^2 - 4 ) = 0`

now for this rational function to be zero . it can only be from the numerator as division by zero is undefined.

`rArr x^2 + x - 12 = 0`
factor and solve.

(x+ 4 )(x - 3 ) = 0 → x = - 4 , x = 3

Similarly , when the function crosses the y-axis , let x = 0.

`rArr y =( -12)/-4 = 3 → y = 3`