Question

What is true of the function g(x) = –2x2 + 5?

g(x) is the multiplication of g and x.
–2x2 +5 is the input of the function.
The variable x represents the independent variable.
The variable g represents the input of th

Answer 1

Given the function \(g(x) = -2x^2 + 5\):

1. **g(x) is the multiplication of g and x:** This statement is incorrect. \( g(x) \) represents the value of the function \(g\) when it is evaluated at \(x\). It does not denote multiplication.

2. **–2x² + 5 is the input of the function:** This statement is incorrect. \(-2x^2 + 5\) is the expression that gives the output of the function \(g\) when you input \(x\). The input is the variable \(x\).

3. **The variable x represents the independent variable:** This statement is correct. In the function \(g(x) = -2x^2 + 5\), \(x\) is the independent variable, which you can choose freely. The value of \(g(x)\) depends on the value chosen for \(x\).

4. **The variable g represents the input of the function:** This statement is incorrect. The variable \(g\) represents the function itself, not the input. The input is the variable \(x\).

In summary, the correct statement is that the variable \(x\) represents the independent variable.