Answer :
To determine which statement best describes the function [tex]\( h(t) = 210 - 15t \)[/tex], it's important to understand the roles of the elements in function notation.
Here’s a detailed explanation:
1. Function Name (h): In the notation [tex]\( h(t) \)[/tex], [tex]\( h \)[/tex] represents the function name. This is the formal way to denote that there is a rule or a relationship being defined.
2. Input (t): The variable inside the parentheses, in this case, [tex]\( t \)[/tex], is the input or independent variable. This is the value for which the function is being evaluated.
3. Output (h(t)): The entire expression [tex]\( h(t) \)[/tex] represents the output or dependent variable. This is the result of applying the function [tex]\( h \)[/tex] to the input [tex]\( t \)[/tex].
Now, let's analyze the given statements:
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 is incorrect because [tex]\( h(t) \)[/tex] is actually the output or dependent variable, not the input.
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. [tex]\( h \)[/tex] is indeed the function name, [tex]\( t \)[/tex] is the input or independent variable, and [tex]\( h(t) \)[/tex] is the output or 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 is incorrect because [tex]\( t \)[/tex] is not the function name; [tex]\( h(t) \)[/tex] is the output or dependent variable, not the input.
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 is incorrect because [tex]\( t \)[/tex] is not the function name; [tex]\( h \)[/tex] is not the input or independent variable.
Given these explanations, the correct statement is:
[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 corresponds to the numerical result [tex]\( 2 \)[/tex].
Here’s a detailed explanation:
1. Function Name (h): In the notation [tex]\( h(t) \)[/tex], [tex]\( h \)[/tex] represents the function name. This is the formal way to denote that there is a rule or a relationship being defined.
2. Input (t): The variable inside the parentheses, in this case, [tex]\( t \)[/tex], is the input or independent variable. This is the value for which the function is being evaluated.
3. Output (h(t)): The entire expression [tex]\( h(t) \)[/tex] represents the output or dependent variable. This is the result of applying the function [tex]\( h \)[/tex] to the input [tex]\( t \)[/tex].
Now, let's analyze the given statements:
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 is incorrect because [tex]\( h(t) \)[/tex] is actually the output or dependent variable, not the input.
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. [tex]\( h \)[/tex] is indeed the function name, [tex]\( t \)[/tex] is the input or independent variable, and [tex]\( h(t) \)[/tex] is the output or 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 is incorrect because [tex]\( t \)[/tex] is not the function name; [tex]\( h(t) \)[/tex] is the output or dependent variable, not the input.
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 is incorrect because [tex]\( t \)[/tex] is not the function name; [tex]\( h \)[/tex] is not the input or independent variable.
Given these explanations, the correct statement is:
[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 corresponds to the numerical result [tex]\( 2 \)[/tex].
