Is a linear function even or odd?
Understand the Problem
The question is asking whether a linear function is classified as even, odd, or neither based on its mathematical properties. To determine this, we will evaluate the function's behavior when its input (x) is replaced with -x and analyze the results.
Answer
A linear function can be even, odd, or neither depending on its form.
The final answer is that a linear function can be even, odd, or neither depending on its specific form. For instance, f(x) = 2x is odd, while f(x) = 2 is even.
Answer for screen readers
The final answer is that a linear function can be even, odd, or neither depending on its specific form. For instance, f(x) = 2x is odd, while f(x) = 2 is even.
More Information
A function is called even if f(x) = f(-x) and called odd if f(-x) = -f(x). Linear functions like f(x) = 2x are odd because 2(-x) = -2x, which is -f(x). However, a constant linear function like f(x) = 2 is even because f(-x) = 2, which is f(x).
Tips
Common mistakes include not correctly identifying the symmetry properties required for even and odd functions. Always substitute -x into the function to check the symmetry.
Sources
- Even and odd functions - Wikipedia - en.wikipedia.org
- How to determine whether a function is even, odd, or neither - kristakingmath.com
- Solved is a linear function even, odd, or neither | Chegg.com - chegg.com
AI-generated content may contain errors. Please verify critical information
