Let's carefully analyze the statement and options given to determine which one best describes the function [tex]\( h(t) = 210 - 15t \)[/tex].
In the standard function notation [tex]\( h(t) \)[/tex], [tex]\( h \)[/tex] is the name of the function, and [tex]\( t \)[/tex] represents the input variable. When we evaluate the function [tex]\( h \)[/tex] at a particular value of [tex]\( t \)[/tex], we get the output [tex]\( h(t) \)[/tex].
To put it more formally:
- [tex]\( h \)[/tex] is the function name.
- [tex]\( t \)[/tex] is the input, or independent variable.
- [tex]\( h(t) \)[/tex] is the output, or dependent variable.
Our task is to identify which statement accurately captures this interpretation:
1. [tex]\( h \)[/tex] is the function name; [tex]\( h(t) \)[/tex] is the input, or independent variable; and [tex]\( t \)[/tex] is the output, or dependent variable.
This statement makes a critical error by labeling [tex]\( h(t) \)[/tex] as the independent variable and [tex]\( t \)[/tex] as the dependent variable, which is incorrect.
2. [tex]\( h \)[/tex] is the function name; [tex]\( t \)[/tex] is the input, or independent variable; and [tex]\( h(t) \)[/tex] is the output, or dependent variable.
This statement is correct. It correctly identifies [tex]\( h \)[/tex] as the function name, [tex]\( t \)[/tex] as the input (independent variable), and [tex]\( h(t) \)[/tex] as the output (dependent variable).
3. [tex]\( t \)[/tex] is the function name; [tex]\( h(t) \)[/tex] is the input, or independent variable; and [tex]\( h \)[/tex] is the output, or dependent variable.
This statement incorrectly labels [tex]\( t \)[/tex] as the function name and swaps the roles of [tex]\( h(t) \)[/tex] and [tex]\( h \)[/tex].
4. [tex]\( t \)[/tex] is the function name; [tex]\( h \)[/tex] is the input, or independent variable; and [tex]\( h(t) \)[/tex] is the output, or dependent variable.
This statement also incorrectly identifies [tex]\( t \)[/tex] as the function name and labels [tex]\( h \)[/tex] as the independent variable.
Thus, the statement that best describes the function [tex]\( h(t) = 210 - 15t \)[/tex] is:
[tex]\[ \boxed{\text{h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.}} \][/tex]
