Question

The hole is (-6,-9) find the rational function which reports this graph​

Answer 1

Explanation:

If there is a hole in the graph at x = -6, that means that there was initially an expression in both the numerator and the denominator that was the same, which is the hole very loosely defined. If the hole is at x = -6, then the factor for that solution is (x + 6). One of those has to be in both the numerator and denominator in order for them to cancel out. This is called a removeable discontinuity. Because the x-intercept is at x = 3, the factor for that zero is (x -3). That has to go in the numerator also. Our equation then for the rational function graphed is

`y=((x+6)(x-3))/((x+6))` which FOILs to

`y=(x^2+3x-18)/(x+6)`