# Educational Material: Understanding Function Descriptions## 1. Complete the Table BelowThis exercise involves filling out a table that transposes symbolic rules of functions into their corresponding verbal descriptions.### Table:| Symbolic Rule | Verbal Description ||---------------|--------------------|| $ f(x) = 3x + 5 $ | The function $ f(x) $ || | The function $ g(x) $ squares the input, then multiplies that result by 2 |### Explanation of Entries:1. **First Row - Symbolic Rule**: - **Function**: $ f(x) $ - **Symbolic Rule**: $ f(x) = 3x + 5 $ - **Verbal Description**: The function $ f(x) $ takes an input number $ x $, multiplies it by 3, and then adds 5 to the result.2. **Second Row - Verbal Description**: - **Function**: $ g(x) $ - **Verbal Description**: The function $ g(x) $ squares the input, then multiplies that result by 2. - **Symbolic Rule**: To find the symbolic rule, let's denote the function $ g(x) $ as performing these operations: 1. Square the input: $ x^2 $ 2. Multiply the squared input by 2: $ 2x^2 $ - Therefore, the symbolic rule can be written as: \[ g(x) = 2x^2 \]By completing the table, students will practice converting between symbolic rules and verbal descriptions of functions, reinforcing their understanding of function notation and operations.

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Answered: 1. Complete the table below. Symbolic…

1. Complete the table below. Symbolic Rule f(x)=3x +5 Verbal Description The function f(x) The function g(x) squares the input, then multiplies that result by 2

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

# Educational Material: Understanding Function Descriptions

## 1. Complete the Table Below

This exercise involves filling out a table that transposes symbolic rules of functions into their corresponding verbal descriptions.

### Table:

| Symbolic Rule | Verbal Description |
|---------------|--------------------|
| $ f(x) = 3x + 5 $ | The function $ f(x) $ |
| | The function $ g(x) $ squares the input, then multiplies that result by 2 |

### Explanation of Entries:

1. **First Row - Symbolic Rule**:
- **Function**: $ f(x) $
- **Symbolic Rule**: $ f(x) = 3x + 5 $
- **Verbal Description**: The function $ f(x) $ takes an input number $ x $, multiplies it by 3, and then adds 5 to the result.

2. **Second Row - Verbal Description**:
- **Function**: $ g(x) $
- **Verbal Description**: The function $ g(x) $ squares the input, then multiplies that result by 2.
- **Symbolic Rule**: To find the symbolic rule, let's denote the function $ g(x) $ as performing these operations:
1. Square the input: $ x^2 $
2. Multiply the squared input by 2: $ 2x^2 $
- Therefore, the symbolic rule can be written as:
\[
g(x) = 2x^2
\]

By completing the table, students will practice converting between symbolic rules and verbal descriptions of functions, reinforcing their understanding of function notation and operations.

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