Question

which table shows a function that is increasing only over the interval (-2, 1), and nowhere else?

x	f(x)
-3	-6
-2	-3
-1	-1
0	1
1	3
2	6

x	f(x)
-3	-2
-2	-4
-1	-1
0	1
1	4
2	3

x	f(x)
-3	-3
-2	-5
-1	-7
0	-6
1	1
2	-1

x	f(x)
-3	5
-2	7
-1	1
0	0
1	-4
2	-2

Explanation:

Step1: Define increasing function

A function is increasing if as x increases, f(x) increases.

Step2: Check first table

x: -3→-2→-1→0→1→2; f(x): -6→-3→-1→1→3→6. Increasing everywhere. Not valid.

Step3: Check second table

x: -3→-2: f(x)-2→-4 (decreasing); -2→-1→0→1: -4→-1→1→4 (increasing); 1→2:4→3 (decreasing). Only increasing on (-2,1). Valid.

Step4: Check third table

x: -3→-2→-1: -3→-5→-7 (decreasing); -1→0→1: -7→-6→1 (increasing);1→2:1→-1 (decreasing). Increasing on (-1,1), not (-2,1). Invalid.

Step5: Check fourth table

x: -3→-2:5→7 (increasing); -2→-1→0→1:7→1→0→-4 (decreasing);1→2:-4→-2 (increasing). Increasing on (-3,-2) and (1,2). Invalid.

Answer:

The second table (with x values -3, -2, -1, 0, 1, 2 and f(x) values -2, -4, -1, 1, 4, 3)