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Think about the function [tex]f(x) = 10 - x^3[/tex].

1. What is the input, or independent variable?

A. [tex]f(x)[/tex]
B. [tex]x[/tex]

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

A. [tex]x[/tex]
B. [tex]f(x)[/tex]

3. What does the notation [tex]f(2)[/tex] mean?

A. Multiply [tex]f[/tex] by 2
B. The output ( [tex]y[/tex]-value) when [tex]x = 2[/tex]
C. The value of [tex]x[/tex] when the output is 2

4. Evaluate [tex]f(2) = \square[/tex].

Sagot :

GinnyAnsweridn
Certainly! Let's explore the given function [tex]\( f(x) = 10 - x^3 \)[/tex] step-by-step.

### 1. Identifying the Input or Independent Variable

For the function [tex]\( f(x) = 10 - x^3 \)[/tex]:
- The input, or independent variable, is [tex]\( x \)[/tex].

### 2. Identifying the Output or Dependent Variable

For the function [tex]\( f(x) = 10 - x^3 \)[/tex]:
- The output, or dependent variable, is [tex]\( f(x) \)[/tex].

### 3. Understanding the Notation [tex]\( f(2) \)[/tex]

The notation [tex]\( f(2) \)[/tex] refers to:
- The output, or the [tex]\( y \)[/tex]-value, when the input [tex]\( x \)[/tex] is equal to 2.

### 4. Evaluating [tex]\( f(2) \)[/tex]

To evaluate [tex]\( f(2) \)[/tex]:
- We substitute [tex]\( x \)[/tex] with 2 in the function [tex]\( f(x) = 10 - x^3 \)[/tex].

Substituting [tex]\( x = 2 \)[/tex] in the function:
[tex]\[ f(2) = 10 - (2)^3 \][/tex]
[tex]\[ f(2) = 10 - 8 \][/tex]
[tex]\[ f(2) = 2 \][/tex]

Therefore, [tex]\( f(2) \)[/tex] evaluates to [tex]\( 2 \)[/tex].

In summary:
- The input, or independent variable, is [tex]\( x \)[/tex].
- The output, or dependent variable, is [tex]\( f(x) \)[/tex].
- The notation [tex]\( f(2) \)[/tex] means the output when [tex]\( x = 2 \)[/tex].
- Evaluating [tex]\( f(2) \)[/tex], we get [tex]\( f(2) = 2 \)[/tex].
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