given the values in the table on the right come from a continuous function, y has at least how many…
given the values in the table on the right come from a continuous function, y has at least how many zeroes?\n0\n1\n2\n3\ndone
Answer
Explanation:
Step1: Check sign - changes
The Intermediate Value Theorem states that for a continuous function (y = f(x)), if (f(a)) and (f(b)) have opposite signs, then there is at least one (c) in the interval ((a,b)) such that (f(c)=0). When (x=-3.2), (y = - 1.19) and when (x=-2.4), (y = 4.62). The sign changes from negative to positive, so there is at least one zero in the interval ((-3.2,-2.4)).
Step2: Check another sign - change
When (x=-0.8), (y=-0.64) and when (x = 0), (y=-5.58), no sign - change. But when (x = 0), (y=-5.58) and when (x = 2.4), (y = 7.26). The sign changes from negative to positive, so there is at least one zero in the interval ((0,2.4)).
Step3: Check the third sign - change
When (x = 1.6), (y=-4.7) and when (x = 2.4), (y = 7.26). The sign changes from negative to positive, so there is at least one zero in the interval ((1.6,2.4)).
Answer:
3