Question

think about the function f(x) = 10 - x^3. what is the input, or independent variable? f(x) x y done what is the output, or dependent variable or quantity? x f(x) y done what does the notation f(2) mean? multiply f by 2 the output (y - value) when x = 2 the value of x when the output is 2 done evaluate f(2) = done

Explanation:

Step1: Identify independent variable

In the function $f(x)=10 - x^{3}$, the independent variable is the input value which can be freely chosen. Here, it is $x$.

Step2: Identify dependent variable

The dependent variable is the output of the function which depends on the value of the independent variable. For $y = f(x)=10 - x^{3}$, the dependent variable is $f(x)$ (or we can also use $y$ to represent the output in a more general - function - as - a - relation context).

Step3: Interpret $f(2)$

The notation $f(2)$ means we substitute $x = 2$ into the function $f(x)$ to find the corresponding output value.

Step4: Evaluate $f(2)$

Substitute $x = 2$ into $f(x)=10 - x^{3}$. So $f(2)=10-2^{3}=10 - 8$.
$f(2)=2$

Answer:

The input, or independent variable is $x$.
The output, or dependent variable is $f(x)$ (or $y$).
The notation $f(2)$ means the output ($y$-value) when $x = 2$.
$f(2)=2$