Final Answer:
The rule and table of values that correspond to points on the graph of the function g‒1(x) are given by the option: A 2-column table with 5 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 1, 2. Column 2 is labeled y with entries negative 14, negative 6, negative 4, negative 2, 6. (a, b) → (‒a, b).
Step-by-step explanation:
The given option represents a transformation of the original function's table of values to its inverse. The function g(x) is transformed to g‒1(x) by negating the x-values while keeping the y-values unchanged. The rule (a, b) → (‒a, b) signifies that each x-value is replaced by its negation, and the y-values remain the same.
In the original table, when x is negative 2, the corresponding y-value is negative 14. Applying the transformation, the inverse function's table has x as 2, and the y-value remains negative 14. This pattern holds for all other entries in the table. The negation of x is reflected in the inverse table while the y-values remain intact.
Mathematically, this transformation can be expressed as g‒1(x) = (‒x, y). For example, when x = 1 in the original function, y = -2, and in the inverse function, when x = -1, y remains -2. This illustrates the concept of inverse functions, where the roles of x and y are swapped. The provided rule and table align with this transformation, demonstrating the inverse relationship between the original function g(x) and its inverse g‒1(x).