Exercise 3 Page 587

We are given the following function and asked to find its $x\text{-}$intercepts. Let's start with recalling that an $x\text{-}$intercept is a point where the graph intersects the $x\text{-}$axis. The $y\text{-}$coordinate of this point is $0.$ Hence, to find the $x\text{-}$intercepts of the given function we can substitute $f(x)$ with $0$ and solve it for $x.$ First, we will rewrite the right-hand side as one rational expression. In order to do this, we will expand the first fraction by $3$ and the second one by $x-1$ so that they have a common denominator. Now we are able to subtract the fractions. The fraction can be equal to $0$ only if its numerator is equal to $0.$ This means that we need to solve the following equation. Let's first change the signs by multiplying both sides of the equation by $\text{-}1.$ Then we will solve it by factoring. According to the Zero Product Property, at least one of the parentheses should be equal to $0.$ We got that the zeroes, or $x\text{-}$intercepts of the function are $\text{-}5$ and $2.$ The answer is D.