Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Given \( k(x) = 6x^0 + x^5 \), answer the following:
**Part: 0 / 4**
**Part 1 of 4**
(a) Find \( k(-x) \).
\[ k(-x) = \square \]
---
**Explanation for Students:**
You are asked to find the function \( k(-x) \) based on the given function \( k(x) = 6x^0 + x^5 \).
1. **Understand the Function:**
- The term \( 6x^0 \) simplifies to 6 because any term to the power of zero is 1.
- \( x^5 \) indicates the presence of a polynomial of degree 5.
2. **Find \( k(-x) \):**
- Substitute \(-x\) into the function \( k(x) \).
- Apply the substitution: \( k(-x) = 6(-x)^0 + (-x)^5 \).
- Simplify the expression using the properties of exponents.
Remember, when substituting, odd powers of \(-x\) will change the sign of the term.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fc2c5a6-892a-41d4-88fb-0ad3e103287c%2Fa0f335e6-92f2-49e3-bee8-f249783168f0%2F43muus_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given \( k(x) = 6x^0 + x^5 \), answer the following:
**Part: 0 / 4**
**Part 1 of 4**
(a) Find \( k(-x) \).
\[ k(-x) = \square \]
---
**Explanation for Students:**
You are asked to find the function \( k(-x) \) based on the given function \( k(x) = 6x^0 + x^5 \).
1. **Understand the Function:**
- The term \( 6x^0 \) simplifies to 6 because any term to the power of zero is 1.
- \( x^5 \) indicates the presence of a polynomial of degree 5.
2. **Find \( k(-x) \):**
- Substitute \(-x\) into the function \( k(x) \).
- Apply the substitution: \( k(-x) = 6(-x)^0 + (-x)^5 \).
- Simplify the expression using the properties of exponents.
Remember, when substituting, odd powers of \(-x\) will change the sign of the term.
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