5 mark for review\nthe table above shows selected values of a continuous function f. for ( 0 leq x leq 13 )…

Explanation:

Step1: Apply Intermediate Value Theorem

The Intermediate Value Theorem states that if a function (y = f(x)) is continuous on a closed interval ([a,b]), and (k) is a number between (f(a)) and (f(b)), then there exists at least one number (c) in the interval ((a,b)) such that (f(c)=k). For the interval ([0,4]): (f(0) = 3) and (f(4)=4.5). Since (3<4<4.5), by the Intermediate - Value Theorem, there is at least one (x_1\in(0,4)) such that (f(x_1) = 4). For the interval ([4,6]): (f(4)=4.5) and (f(6)=3). Since (3<4<4.5), by the Intermediate - Value Theorem, there is at least one (x_2\in(4,6)) such that (f(x_2)=4). For the interval ([8,13]): (f(8) = 2.5) and (f(13)=4.4). Since (2.5<4<4.4), by the Intermediate - Value Theorem, there is at least one (x_3\in(8,13)) such that (f(x_3)=4).

Answer:

C. three