Question

Given the function f(x) with its values over intervals, determine the valid prediction about f(x).

(A) ( f(x) < 0 ) over the interval ( (-[infinity], 0) ).
(B) ( f(x) > 0 ) over the interval ( (-1, 0) ).
(C) ( f(x) > 0 ) over the interval ( [-1, 1) ).
(D) ( f(x) < 0 ) over the interval ( (0, 2) ).

Answer 1

The valid predictions about the function f(x) are (A) ( f(x) < 0 ) over the interval ( (-[infinity], 0) ) and (D) ( f(x) < 0 ) over the interval ( (0, 2) ).

Step-by-step explanation:

The given function f(x) is a horizontal line between x = 0 and x = 20, inclusive. Since the function is a horizontal line, its values will remain constant throughout the interval. Therefore, the valid predictions about the function f(x) are:

1. (A) ( f(x) < 0 ) over the interval ( (-[infinity], 0) ): Since the function is a horizontal line and its values are constant, if the values are below 0 before x = 0, then f(x) < 0 is a valid prediction.
2. (D) ( f(x) < 0 ) over the interval ( (0, 2) ): Since the function is a horizontal line and its values are constant, if the values are below 0 between x = 0 and x = 2, then f(x) < 0 is a valid prediction.