Exercise 10 Page 693

The zeros of a function are the points where the graph intersects the x-axis. Let's take a look at our function. f(x)=x^2-x-12/x-2 Once simplified, a rational function has zeros at the values that make the numerator 0. Therefore, to find the zeros we need to complete the following steps.

1. Substitute 0 for f(x) in the function rule.
2. Simplify the function rule by dividing out any common factors between the numerator and the denominator.
3. Solve for x.

Note that in this case there are no common factors between the expressions in the numerator and the denominator, so we can skip the second step.

To solve the resulting quadratic equation we need to factor the trinomial. Once the expression is written in factored form, we can apply the Zero Product Property.

The numerator is 0, and therefore f(x)=0 when x=4 or x=- 3. This means that the zeros of the function are - 3 and 4.