Let's analyze each statement using the given table of values for [tex]\( f(x) \)[/tex] step-by-step.
### Statement A: [tex]\( f(0) = 10 \)[/tex]
First, we look at the table to find the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex].
- According to the table, when [tex]\( x = 0 \)[/tex], [tex]\( f(0) = 3 \)[/tex].
Therefore, the statement [tex]\( f(0) = 10 \)[/tex] is false.
### Statement B: The range for [tex]\( f(x) \)[/tex] is all real numbers
To determine if this statement is true, we need to look at the range of values [tex]\( f(x) \)[/tex] takes in the table:
- The table shows that [tex]\( f(x) \)[/tex] takes on the values {1, 2, 3, 0}.
The range of [tex]\( f(x) \)[/tex] is {0, 1, 2, 3}. This set does not include all real numbers.
Therefore, the statement that the range for [tex]\( f(x) \)[/tex] is all real numbers 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]
To verify this, we need to check the [tex]\( x \)[/tex]-values provided in the table. The [tex]\( x \)[/tex]-values given are:
- {-5, -3, 0, 2, 6, 7, 9, 10, 13}
These values match exactly with the set described in the statement.
Therefore, the statement that the domain for [tex]\( f(x) \)[/tex] is the set [tex]\(\{-5, -3, 0, 2, 6, 7, 9, 10, 13\}\)[/tex] is true.
### Statement D: [tex]\( f(-3) = 2 \)[/tex]
Next, we check the value of [tex]\( f(x) \)[/tex] when [tex]\( x = -3 \)[/tex] from the table:
- According to the table, when [tex]\( x = -3 \)[/tex], [tex]\( f(-3) = 2 \)[/tex].
Therefore, the statement [tex]\( f(-3) = 2 \)[/tex] is true.
### Conclusion
Putting this all together:
- Statement A: False
- Statement B: False
- Statement C: True
- Statement D: True
Thus, the correct markings for the statements are:
- A. False
- B. False
- C. True
- D. True
