Question

What is the zero of the function?

f(x)=x2−x−6/x2−8x+15

Answer 1

Rational Function: any function that is found by a rational fraction.

Its form:
`(1)/(x)`

Finding Zeros of a Rational Function:

1. Factor Numerator and denominator

`f(x)=((x-3)(x+2))/((x-5)(x-3))`

2. Find restrictions by equating the denominator to 0

`x-5=0`
`x-3=0` when x=-5 and 3, the function is undefined

`x=-5`
`x=3`

3. Set the numerator equal to zero

`x-3=0`
`x+2=0`

`x=3`
`x=-2`

Be careful - since we have x-3 on both the numerator and denominator the graph will not intersect the x-axis at that point. This is what is called a removable discontinuity.

Therefore, the only zero occurs at (-2,0)