Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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# 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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Transcribed Image Text:# 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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