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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could you please show how u found the correct answer as well as showing each step for the problem.
![**Question 7**
Determine if the given function is even, odd, or neither.
\[ P(x) = -3x^5 - 8x^3 - x + 1 \]
- ○ odd function
- ○ neither even nor odd
- ○ even function
**Explanation:**
This question requires determining if the function \( P(x) = -3x^5 - 8x^3 - x + 1 \) is an even function, an odd function, or neither.
- **Even Function**: A function is even if \( f(x) = f(-x) \) for all \( x \) in the domain.
- **Odd Function**: A function is odd if \( f(-x) = -f(x) \) for all \( x \) in the domain.
To verify, substitute \(-x\) into the function and compare \( P(-x) \) with \( P(x) \) and \(-P(x) \).
This information can help students understand whether a function is even, odd, or neither by examining symmetry and applying algebraic checks.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4643730-756f-4385-a96d-a4c90bcc91eb%2Ff08ebe9c-2334-4f44-9955-8925fe6c893c%2Fncq3r2i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 7**
Determine if the given function is even, odd, or neither.
\[ P(x) = -3x^5 - 8x^3 - x + 1 \]
- ○ odd function
- ○ neither even nor odd
- ○ even function
**Explanation:**
This question requires determining if the function \( P(x) = -3x^5 - 8x^3 - x + 1 \) is an even function, an odd function, or neither.
- **Even Function**: A function is even if \( f(x) = f(-x) \) for all \( x \) in the domain.
- **Odd Function**: A function is odd if \( f(-x) = -f(x) \) for all \( x \) in the domain.
To verify, substitute \(-x\) into the function and compare \( P(-x) \) with \( P(x) \) and \(-P(x) \).
This information can help students understand whether a function is even, odd, or neither by examining symmetry and applying algebraic checks.
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