Math Problem Statement
Solution
The problem in your image asks you to fill out the table of values for three functions and determine whether each function is even, odd, or neither. Here's a breakdown of the functions provided:
To determine if a function is even, odd, or neither, we need to follow these rules:
- A function is even if for all .
- A function is odd if for all .
- If neither condition holds, then the function is neither.
Let's start by analyzing the functions:
1.
This is a polynomial function, and we can determine its symmetry by testing :
- Since , the function is even.
2.
For trigonometric functions, recall:
- So,
- Since and , this function is neither.
3.
For the tangent function, recall:
- Thus,
- Since , the function is odd.
Now you can complete the table
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Math Problem Analysis
Mathematical Concepts
Even and Odd Functions
Trigonometry
Polynomial Functions
Formulas
f(x) = -x^6 + 3x^2
f(x) = sin(x) + 3
f(x) = tan(x)
Theorems
A function is even if f(-x) = f(x)
A function is odd if f(-x) = -f(x)
Suitable Grade Level
Grades 10-12
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