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

which table shows a function that is increasing only over the interval (-2, 1), and nowhere else?\n| x | f(x) | | x | f(x) | | x | f(x) |\n| -3 | -6 | | -3 | -2 | | -3 | -3 |\n| -2 | -3 | | -2 | -4 | | -2 | -5 |\n| -1 | -1 | | -1 | -1 | | -1 | -7 |\n| 0 | 1 | | 0 | 1 | | 0 | -6 |\n| 1 | 3 | | 1 | 4 | | 1 | 1 |\n| 2 | 6 | | 2 | 3 | | 2 | -1 |\n| x | f(x) |\n| -3 | 5 |\n| -2 | 7 |\n| -1 | 1 |\n| 0 | 0 |\n| 1 | -4 |\n| 2 | -2 |

which table shows a function that is increasing only over the interval (-2, 1), and nowhere else?\n| x | f(x) | | x | f(x) | | x | f(x) |\n| -3 | -6 | | -3 | -2 | | -3 | -3 |\n| -2 | -3 | | -2 | -4 | | -2 | -5 |\n| -1 | -1 | | -1 | -1 | | -1 | -7 |\n| 0 | 1 | | 0 | 1 | | 0 | -6 |\n| 1 | 3 | | 1 | 4 | | 1 | 1 |\n| 2 | 6 | | 2 | 3 | | 2 | -1 |\n| x | f(x) |\n| -3 | 5 |\n| -2 | 7 |\n| -1 | 1 |\n| 0 | 0 |\n| 1 | -4 |\n| 2 | -2 |

Answer

Explanation:

Step1: Check first table

For (x) values from (-3) to (-2), (f(x)) changes from (-6) to (-3) (increasing). From (-2) to (1), (f(x)) continues increasing ((-3) to (3)). From (1) to (2), (f(x)) increases from (3) to (6). So it increases not only on ((-2,1)).

Step2: Check second table

For (x=-3) to (x = - 2), (f(x)) changes from (-2) to (-4) (decreasing). From (x=-2) to (x = 1), (f(x)) increases ((-4) to (4)). From (x = 1) to (x=2), (f(x)) decreases from (4) to (3). This function increases only on ((-2,1)).

Step3: Check third table

For (x=-3) to (x=-2), (f(x)) changes from (-3) to (-5) (decreasing). From (x=-2) to (x = 0), (f(x)) decreases ((-5) to (-6)). From (x = 0) to (x=1), (f(x)) increases ((-6) to (1)). From (x = 1) to (x = 2), (f(x)) decreases from (1) to (-1). It does not increase only on ((-2,1)).

Step4: Check fourth table

For (x=-3) to (x=-2), (f(x)) changes from (5) to (7) (increasing). From (x=-2) to (x=-1), (f(x)) decreases ((7) to (1)). It does not increase only on ((-2,1)).

Answer:

The second - table (from left - to - right) shows a function that is increasing only over the interval ((-2,1)) and nowhere else.