Let's evaluate the given statements based on the table provided:
### Statement A: [tex]\( f(-3) = 2 \)[/tex]
Looking at the table, when [tex]\( x = -3 \)[/tex], the value of [tex]\( f(x) \)[/tex] is 2. Therefore, [tex]\( f(-3) = 2 \)[/tex] is a true statement.
### Statement B: The range for [tex]\( f(x) \)[/tex] is all real numbers
The range of a function is the set of all possible output values (y-values). From the table, the output values (y-values) are \{1, 2, 3, 0, 1, 2, 3, 0, 1\}. The unique values here are \{0, 1, 2, 3\}. Since the range only includes 0, 1, 2, and 3, it is not all real numbers. Hence, this statement is false.
### Statement C: [tex]\( f(0) = 10 \)[/tex]
Checking the table, when [tex]\( x = 0 \)[/tex], the value of [tex]\( f(x) \)[/tex] is 3, not 10. Therefore, [tex]\( f(0) = 10 \)[/tex] is a false statement.
### Statement D: The domain for [tex]\( f(x) \)[/tex] is the set [tex]\(\{-5, -3, 0, 2, 6, 7, 9, 10, 13\}\)[/tex]
The domain of a function is the set of all possible input values (x-values). From the table, the x-values are \{-5, -3, 0, 2, 6, 7, 9, 10, 13\}. This exactly matches the set given in the statement. Therefore, this statement is true.
### Conclusion
Based on the evaluation, the true statements are:
- A. [tex]\( f(-3) = 2 \)[/tex]
- D. The domain for [tex]\( f(x) \)[/tex] is the set [tex]\(\{-5, -3, 0, 2, 6, 7, 9, 10, 13\}\)[/tex]
Thus, the answers are:
- [tex]\( ( \text{True, False, False, True} ) \)[/tex]
