Question

think about the function ( f(x) = 10 - x^2 ).
what is the input, or independent variable?
( circ ) ( f(x) )
( circ ) ( x )
( circ ) ( y )
( \boldsymbol{circ} ) done

what is the output, or dependent variable or quantity?
( circ ) ( x )
( circ ) ( f(x) )
( circ ) ( y )
( \boldsymbol{circ} ) done

what does the notation ( f(2) ) mean?
( circ ) multiply ( f ) by 2
( circ ) the output (y - value) when ( x = 2 )
( circ ) the value of ( x ) when the output is 2
( \boldsymbol{circ} ) done

evaluate ( f(2) = square )
( \boldsymbol{circ} ) done

Explanation:

Part 1: Input (Independent Variable)

In a function \( f(x) \), the input (independent variable) is the variable inside the function notation, which is \( x \). The function \( f(x) \) takes \( x \) as input and produces an output.

The output (dependent variable) of a function \( f(x) \) is the result of the function, which can be represented as \( f(x) \) (or also \( y \) since \( y = f(x) \) in many cases). Here, \( f(x) \) is the expression that gives the output based on the input \( x \).

The notation \( f(2) \) in a function \( f(x) \) means we substitute \( x = 2 \) into the function and find the corresponding output (the \( y \)-value when \( x = 2 \)). It is not multiplying \( f \) by 2, nor is it finding \( x \) when output is 2 (that would be solving \( f(x)=2 \) for \( x \)).

Answer:

\( x \)

Part 2: Output (Dependent Variable)