To determine the truth of the statements, let's analyze the given table of values for y = f(X):
X | y = f(X)
-5 | 0
-3 | 2
0 | 6
2 | 7
6 | 9
7 | 10
9 | 13
Statement A: "The range for f(x) is all real numbers."
To find the range of the function, we need to consider all the output values (y-values) in the table. In this case, the range of f(x) is the set of all distinct y-values: {0, 2, 6, 7, 9, 10, 13}. This set contains real numbers but is not all real numbers. Therefore, statement A is false.
Statement B: "The domain for f(x) is the set (-5, -3, 0, 2, 6, 7, 9, 10, 13)."
The domain of a function represents all the input values (x-values) for which the function is defined. Looking at the table, we can see that the given domain is {-5, -3, 0, 2, 6, 7, 9}. The values 10 and 13 are not part of the domain since they do not have corresponding x-values in the table. Therefore, statement B is false.
To summarize, neither statement A nor statement B is true based on the given table of values.