Let's analyze each statement one by one based on the provided table.
### Statement A: [tex]\( f(-3) = 2 \)[/tex]
From the table, when [tex]\( x = -3 \)[/tex]:
[tex]\[
f(-3) = 2
\][/tex]
This statement is true.
### 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. From the table, the values of [tex]\( f(x) \)[/tex] are:
[tex]\[
1, 2, 3, 0, 1, 2, 3, 0, 1
\][/tex]
The unique values are:
[tex]\[
\{0, 1, 2, 3\}
\][/tex]
Since the range only includes these four specific values, it is not all real numbers. Therefore, this statement is false.
### Statement C: 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. From the table, the [tex]\( x \)[/tex]-values are:
[tex]\[
-5, -3, 0, 2, 6, 7, 9, 10, 13
\][/tex]
These values match exactly the given set. Therefore, this statement is true.
### Statement D: [tex]\( f(0) = 10 \)[/tex]
From the table, when [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 3
\][/tex]
This statement claims that [tex]\( f(0) \)[/tex] is 10, which is not true. Therefore, this statement is false.
### Summary
1. Statement A: True
2. Statement B: False
3. Statement C: True
4. Statement D: False
Thus, the correct results are [tex]\(\boxed{\text{True, False, True, False}}\)[/tex].
