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What is true of the function [tex]\( g(x) = -2x^2 + 5 \)[/tex]?

A. [tex]\( g(x) \)[/tex] is the multiplication of [tex]\( g \)[/tex] and [tex]\( x \)[/tex].
B. [tex]\( -2x^2 + 5 \)[/tex] is the input of the function.
C. The variable [tex]\( x \)[/tex] represents the independent variable.
D. The variable [tex]\( g \)[/tex] represents the input of the function.

Sagot :

GinnyAnswer
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.
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