Questions and Answers
Is the function f(x) = x⁵ + x³ + 1 even, odd, or neither?
Neither
Is the function f(x) = x⁵ + x³ even, odd, or neither?
Odd
Is the function f(x) = x⁷ - x³ + 5 even, odd, or neither?
Neither
Is the function f(x) = x⁶ + x² + 3 even, odd, or neither?
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Is the function f(x) = x² + 3 even, odd, or neither?
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Is the function f(x) = (x + 3)³ even, odd, or neither?
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Is the function f(x) = |x| + 1 even, odd, or neither?
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Is the function f(x) = 2x⁷ - 4x even, odd, or neither?
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Is the function f(x) = -x⁵ + x³ + x even, odd, or neither?
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Is the function f(x) = x⁴ + x² even, odd, or neither?
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Is the function f(x) = 10x³ even, odd, or neither?
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Is the function f(x) = 2x⁵ - 5 even, odd, or neither?
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Study Notes
Even and Odd Functions
- A function is even if f(-x) = f(x) for all x in the domain.
- A function is odd if f(-x) = -f(x) for all x in the domain.
- A function is classified as neither if it does not satisfy the conditions for either even or odd.
Function Classifications
-
f(x) = x⁵ + x³ + 1
- Classification: Neither
-
f(x) = x⁵ + x³
- Classification: Odd
-
f(x) = x⁷ - x³ + 5
- Classification: Neither
-
f(x) = x⁶ + x² + 3
- Classification: Even
-
f(x) = x² + 3
- Classification: Even
-
f(x) = (x + 3)³
- Classification: Neither
-
f(x) = |x| + 1
- Classification: Even
-
f(x) = 2x⁷ - 4x
- Classification: Odd
-
f(x) = -x⁵ + x³ + x
- Classification: Odd
-
f(x) = x⁴ + x²
- Classification: Even
-
f(x) = 10x³
- Classification: Odd
-
f(x) = 2x⁵ - 5
- Classification: Neither
Summary of Classifications
- Functions such as x⁶ + x² + 3, x² + 3, |x| + 1, x⁴ + x², and 10x³ are classified as even functions due to their symmetry about the y-axis.
- Functions like x⁵ + x³, 2x⁷ - 4x, and -x⁵ + x³ + x are classified as odd functions, showing rotational symmetry around the origin.
- Complex functions like x⁵ + x³ + 1 and other forms demonstrated that not all functions fall into even or odd categories; they can be classified as neither.
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Test your understanding of even and odd functions with these flashcards. Determine whether the given functions are even, odd, or neither based on their algebraic expressions. Perfect for students learning about function properties in algebra.
