what is the answer of construct the table of signs of y=(x-3)(x+4)(x+7)
Answer (1)
Answer:To construct the table of signs for the function , follow these steps:1. Identify the critical points (roots):The function is a product of three factors. Set each factor equal to zero to find the roots:The critical points (where the function equals zero) are: , , and .2. Determine the sign of the function in each interval:The roots divide the number line into four intervals:Now, we will test the sign of in each interval by choosing a test point from each interval and checking whether the product of the three factors is positive or negative.3. Check the sign in each interval:Interval :Choose :(x - 3) = -8 - 3 = -11,\quad (x + 4) = -8 + 4 = -4,\quad (x + 7) = -8 + 7 = -1Interval :Choose :(x - 3) = -5 - 3 = -8,\quad (x + 4) = -5 + 4 = -1,\quad (x + 7) = -5 + 7 = 2Interval :Choose :(x - 3) = 0 - 3 = -3,\quad (x + 4) = 0 + 4 = 4,\quad (x + 7) = 0 + 7 = 7Interval :Choose :(x - 3) = 4 - 3 = 1,\quad (x + 4) = 4 + 4 = 8,\quad (x + 7) = 4 + 7 = 114. Construct the table of signs:At , , and , the function because these are the roots.Thus, the function is negative in the intervals and , and positive in the intervals and .
