Exercise 3 Page 587

We are given the following function and asked to find its x-intercepts. f(x)=2/x-1-x+4/3 Let's start with recalling that an x-intercept is a point where the graph intersects the x-axis. The y-coordinate of this point is 0. Hence, to find the x-intercepts of the given function we can substitute f(x) with 0 and solve it for x. 0=2/x-1-x+4/3First, 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. 0=2( 3)/3(x-1)-(x+4)(x-1)/3(x-1) 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. - x^2-3x+10=0 Let's first change the signs by multiplying both sides of the equation by - 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. lx-2=0 x+5=0 ⇒ lx=2 x=- 5 We got that the zeroes, or x-intercepts of the function are - 5 and 2. The answer is D.