Answer :
To determine the correct statement about the function [tex]\( g(x) = -2x^2 + 5 \)[/tex], let's analyze each option step by step:
1. [tex]\( g(x) \)[/tex] is the multiplication of [tex]\( g \)[/tex] and [tex]\( x \)[/tex].
This is not true. In the context of functions, [tex]\( g(x) \)[/tex] is notation that represents the value of the function [tex]\( g \)[/tex] at a specific input [tex]\( x \)[/tex]. It doesn't imply multiplication of [tex]\( g \)[/tex] and [tex]\( x \)[/tex].
2. [tex]\( -2x^2 + 5 \)[/tex] is the input of the function.
This is also incorrect. The expression [tex]\( -2x^2 + 5 \)[/tex] represents the output or value of the function, not the input. The input of the function is [tex]\( x \)[/tex].
3. The variable [tex]\( x \)[/tex] represents the independent variable.
This statement is true. In the function [tex]\( g(x) = -2x^2 + 5 \)[/tex], [tex]\( x \)[/tex] is the independent variable, which means it is the variable that can be freely changed, and it determines the output of the function.
4. The variable [tex]\( g \)[/tex] represents the input of the function.
This is incorrect. The variable [tex]\( g \)[/tex] in the notation [tex]\( g(x) \)[/tex] refers to the function itself, not the input. The input is represented by [tex]\( x \)[/tex].
Among the given options, the correct statement is:
The variable [tex]\( x \)[/tex] represents the independent variable.
So, the correct statement number is:
3.
1. [tex]\( g(x) \)[/tex] is the multiplication of [tex]\( g \)[/tex] and [tex]\( x \)[/tex].
This is not true. In the context of functions, [tex]\( g(x) \)[/tex] is notation that represents the value of the function [tex]\( g \)[/tex] at a specific input [tex]\( x \)[/tex]. It doesn't imply multiplication of [tex]\( g \)[/tex] and [tex]\( x \)[/tex].
2. [tex]\( -2x^2 + 5 \)[/tex] is the input of the function.
This is also incorrect. The expression [tex]\( -2x^2 + 5 \)[/tex] represents the output or value of the function, not the input. The input of the function is [tex]\( x \)[/tex].
3. The variable [tex]\( x \)[/tex] represents the independent variable.
This statement is true. In the function [tex]\( g(x) = -2x^2 + 5 \)[/tex], [tex]\( x \)[/tex] is the independent variable, which means it is the variable that can be freely changed, and it determines the output of the function.
4. The variable [tex]\( g \)[/tex] represents the input of the function.
This is incorrect. The variable [tex]\( g \)[/tex] in the notation [tex]\( g(x) \)[/tex] refers to the function itself, not the input. The input is represented by [tex]\( x \)[/tex].
Among the given options, the correct statement is:
The variable [tex]\( x \)[/tex] represents the independent variable.
So, the correct statement number is:
3.
