Question

Think about the function f(x) = 10 - x3. What is the input, or independent variable? f(x) x y What is the output, or dependent variable or quantity? x f(x) y 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 Evaluate f(2) =

Answer 1

Answer:

x is the input, or independent variable and f(x) is the output, or dependent variable or quantity. f(2) represents the output (y-value) when x = 2. The value of f(2) is 2.

Step-by-step explanation:

If the values of a variable depends on the other variable, then it called dependent variable.

If the value of a variable does not depend on the other, then it is called independent variable.

If a function is f(x)=x, then x is an independent variable and f(x) is a dependent variable.

The given function is

$f(x)=10-x^3$

Here, x is the input, or independent variable and f(x) is the output, or dependent variable or quantity.

The notation f(a) represents the output (y-value) when x = a. So, f(2) represents the output (y-value) when x = 2.

Substitute x=2 in the given function.

$f(2)=10-(2)^3$

$f(2)=10-8$

$f(2)=2$

The value of f(2) is 2.

Answer 2

For a function y = f(x) we define x as the independent variable and y as the dependent variable. y = f(x) means that "y depends on x in a given way, defined by f(x)".

Here we know that:

f(x) = 10 - x^3

1) What is the input, or independent variable?

The independent variable is the one inside the function, in this case, is x.

2) What is the output, or dependent variable or quantity?

in this case, the output is f(x), the value of the whole function evaluated in x.

(note that we do not have y = f(x), so y can't be the output, as we can't invent a variable and add it there.)

3) What does f(2) mean?

This means that we need to replace all the "x's" in the function by 2, we get:

f(2) = 10 - 2^3 = 2

so f(2) is the output when x = 2.

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