Use the graph of the function to determine whether the function is even, odd, c f(x) = 2x + tan x The function is even. O The function is odd. O The function is neither even nor odd.
Use the graph of the function to determine whether the function is even, odd, c f(x) = 2x + tan x The function is even. O The function is odd. O The function is neither even nor odd.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![### Identifying the Nature of a Trigonometric Function
#### Problem Statement:
**LARTRIG10 1.6.061**
*Use the graph of the function to determine whether the function is even, odd, or neither.*
\[ f(x) = 2x + \tan x \]
#### Options:
- [ ] The function is even.
- [ ] The function is odd.
- [ ] The function is neither even nor odd.
To solve this problem, analyze the graph of the given function \( f(x) = 2x + \tan x \). Recall the definitions:
- **Even Function**: A function is even if \( f(-x) = f(x) \).
- **Odd Function**: A function is odd if \( f(-x) = -f(x) \).
When studying the graph, check for symmetry about the y-axis (signifying an even function) or origin (signifying an odd function). If neither symmetry is present, the function is neither even nor odd.
#### Instructions for Educational Use:
- **Upload the graph** of \( f(x) = 2x + \tan x \) to visually inspect the symmetry properties.
- **Analyze the symmetry**:
- Symmetry about the y-axis indicates the function is even.
- Symmetry about the origin indicates the function is odd.
- The absence of both symmetries suggests the function is neither even nor odd.
Evaluate the function for \( x \) and \( -x \) to algebraically determine its nature, complementing the graphical analysis.
This content helps learners understand how to analyze functions graphically and algebraically to determine their symmetry properties, vital for mastering trigonometric functions' behavior in various applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bf5cc85-f331-41fb-a902-3c0ed5d3d96d%2Fc08aaca2-e2ab-4b20-8335-32ec1c31d5cf%2Fj1z2cdx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Identifying the Nature of a Trigonometric Function
#### Problem Statement:
**LARTRIG10 1.6.061**
*Use the graph of the function to determine whether the function is even, odd, or neither.*
\[ f(x) = 2x + \tan x \]
#### Options:
- [ ] The function is even.
- [ ] The function is odd.
- [ ] The function is neither even nor odd.
To solve this problem, analyze the graph of the given function \( f(x) = 2x + \tan x \). Recall the definitions:
- **Even Function**: A function is even if \( f(-x) = f(x) \).
- **Odd Function**: A function is odd if \( f(-x) = -f(x) \).
When studying the graph, check for symmetry about the y-axis (signifying an even function) or origin (signifying an odd function). If neither symmetry is present, the function is neither even nor odd.
#### Instructions for Educational Use:
- **Upload the graph** of \( f(x) = 2x + \tan x \) to visually inspect the symmetry properties.
- **Analyze the symmetry**:
- Symmetry about the y-axis indicates the function is even.
- Symmetry about the origin indicates the function is odd.
- The absence of both symmetries suggests the function is neither even nor odd.
Evaluate the function for \( x \) and \( -x \) to algebraically determine its nature, complementing the graphical analysis.
This content helps learners understand how to analyze functions graphically and algebraically to determine their symmetry properties, vital for mastering trigonometric functions' behavior in various applications.
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