To determine which statement could be true for the function [tex]\( h \)[/tex], let's analyze each option given the information about the function's domain, range, and specific values.
### Information Given:
1. Domain of [tex]\( h \)[/tex]: [tex]\(-3 \leq x \leq 11\)[/tex]
2. Range of [tex]\( h \)[/tex]: [tex]\(1 \leq h(x) \leq 25\)[/tex]
3. Specific points: [tex]\( h(8) = 19 \)[/tex] and [tex]\( h(-2) = 2 \)[/tex]
### Analyzing Each Statement:
A. [tex]\( n(8) = 21 \)[/tex]
- This statement defines a function [tex]\( n \)[/tex], not [tex]\( h \)[/tex]. Since [tex]\( n \)[/tex] is not the function we are given, the statement is irrelevant to what we are analyzing.
B. [tex]\( h(-3) = -1 \)[/tex]
- The value [tex]\(-1\)[/tex] is outside the given range of the function [tex]\( h \)[/tex], which is [tex]\( 1 \leq h(x) \leq 25 \)[/tex]. Therefore, this statement is false.
C. [tex]\( h(13) = 18 \)[/tex]
- The value [tex]\( 13 \)[/tex] is outside the given domain of the function [tex]\( h \)[/tex], which is [tex]\(-3 \leq x \leq 11 \)[/tex]. Therefore, this statement cannot be true.
D. [tex]\( f(2) = 16 \)[/tex]
- This statement defines a function [tex]\( f \)[/tex], not [tex]\( h \)[/tex]. Since [tex]\( f \)[/tex] is not the function we are given, the statement is unrelated.
### Conclusion:
After analyzing each statement considering the given properties of the function [tex]\( h \)[/tex], none of the statements (A, B, C, or D) could be true for the function [tex]\( h \)[/tex].
Therefore, the answer is:
[tex]\[ 0 \][/tex]
None of the statements could be true.
