Answers:
Choice A(-2,-1)
Choice B(-1,0)
Choice E(2,3)
--------------------------------
Step-by-step explanation:
The idea is to look for sign changes in f(x). Recall that y = f(x). If the sign of y changes, then y = 0 must be somewhere in the interval if we are to have a continuous function.
The sign changes happen when we go from...
y = -9 to y = +8 (row 2 to row 3)
y = +8 to y = -5 (row 3 to row 4)
y = -1 to y = +196 (bottom two rows)
Those three sign changes correspond to the following interval notations for x
(-2,-1)
(0,1)
(2,3)
in that exact order
Meaning for instance, that a root must be somewhere in the interval -2 < x < -1 since we have a sign change when we transition from f(-2) to f(-1)
So that's why the answers are choices A, B, & E
Something like the interval notation (1,2) will not work because y = -18 does not change sign to y = -1, which is why D is not an answer. Choice C is similar.