Determining Even or Odd Functions
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Questions and Answers

Determine if the function f(x) = x2 + 5 is Even, Odd, or Neither.

  • Even, since f(x) = -f(-x)
  • Neither, since f(x) ≠ f(-x) and f(-x) ≠ - f(x)
  • Odd, since f(x) = -f(-x)
  • Even, since f(x) = f(-x) (correct)

Determine if the function f(x) = x + 15 is Even, Odd, or Neither.

  • Odd, since f(x) = -f(-x)
  • Even, since f(x) = f(-x)
  • Neither, since f(x) ≠ f(-x) and f(-x) ≠ - f(x) (correct)
  • Odd, since f(x) = f(-x)

Determine if the function f(x) = x2 + x3 + 10 is Even, Odd, or Neither.

  • Odd, since f(x) = -f(-x)
  • Neither, since f(x) ≠ f(-x) and f(-x) ≠ -f(x) (correct)
  • Even, since f(x) = f(-x)
  • Even, since f(x) = -f(-x)

Determine if the function f(x) = -x3 is Even, Odd, or Neither.

<p>Odd, since f(x) = -f(-x) (A)</p> Signup and view all the answers

Determine if the function f(x) = x2 - x4 is Even, Odd, or Neither.

<p>Even, since f(x) = f(-x) (A)</p> Signup and view all the answers

Determine if the function f(x) = 9 + x + x2 is Even, Odd, or Neither.

<p>Neither, since f(x) ≠ f(-x) and f(-x) ≠ -f(x) (D)</p> Signup and view all the answers

Determine if the function f(x) = x2 + x6 + x10 is Even, Odd, or Neither.

<p>Even, since f(x) = f(-x) (A)</p> Signup and view all the answers

Determine if the function f(x) = x + x3 + x5 is Even, Odd, or Neither.

<p>Odd, since f(x) = -f(-x) (D)</p> Signup and view all the answers

Determine if the function f(x) = sin x + 2 is Even, Odd, or Neither.

<p>Neither, since f(x) ≠ f(-x) and f(-x) ≠ -f(x) (B)</p> Signup and view all the answers

Determine if the function f(x) = sin(x2) is Even, Odd, or Neither.

<p>Even, since f(x) = f(-x) (C)</p> Signup and view all the answers

Determine if the function f(x) = sin(-x) is Even, Odd, or Neither.

<p>Odd, since f(x) = -f(-x) (D)</p> Signup and view all the answers

Determine if the function f(x) = cos(x) + sin(x) * 3 is Even, Odd, or Neither.

<p>Neither, since f(x) ≠ f(-x) and f(-x) ≠ - f(x) (D)</p> Signup and view all the answers

Determine if the function f(x) = cos(x) + x is Even, Odd, or Neither.

<p>Neither, since f(x) ≠ f(-x) and f(-x) ≠ - f(x) (D)</p> Signup and view all the answers

Flashcards

Even Function

A function is even if replacing x with -x results in the original function. Mathematically, f(-x) = f(x).

Odd Function

A function is odd if replacing x with -x results in the negative of the original function. Mathematically, f(-x) = -f(x).

Neither Even nor Odd Function

A function that does not satisfy the conditions of being either even or odd.

Is f(x) = x^2 + 5 even, odd, or neither?

The function f(x) = x^2 + 5 is an even function because f(-x) = (-x)^2 + 5 = x^2 + 5 = f(x).

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Is f(x) = x + 15 even, odd, or neither?

The function f(x) = x + 15 is neither even nor odd because f(-x) = -x + 15 and -f(x) = -x - 15.

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Is f(x) = x^7 even, odd, or neither?

The function f(x) = x^7 is an odd function because f(-x) = (-x)^7 = -x^7 = -f(x).

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Is f(x) = x^3 - 15 even, odd, or neither?

The function f(x) = x^3 - 15 is an odd function because f(-x) = (-x)^3 - 15 = -x^3 - 15 = -f(x).

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Is f(x) = x^4 + x^3 + 10 even, odd, or neither?

The function f(x) = x^4 + x^3 + 10 is neither even nor odd because f(-x) = x^4 - x^3 + 10 and neither this result nor its negative matches the original function.

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Is f(x) = x^2 even, odd, or neither?

The function f(x) = x^2 is an even function because f(-x) = (-x)^2 = x^2 = f(x).

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Is f(x) = -x^2 even, odd, or neither?

The function f(x) = -x^2 is an even function because f(-x) = -(-x)^2 = -x^2 = f(x).

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Is f(x) = x^3 even, odd, or neither?

The function f(x) = x^3 is an odd function because f(-x) = (-x)^3 = -x^3 = -f(x).

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Is f(x) = -x^3 even, odd, or neither?

The function f(x) = -x^3 is an odd function because f(-x) = -(-x)^3 = x^3 = -f(x).

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Is f(x) = x^4 + x^2 + x - 5 even, odd, or neither?

The function f(x) = x^4 + x^2 + x - 5 is neither even nor odd because f(-x) = x^4 + x^2 - x - 5 and neither this result nor its negative matches the original function.

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Is f(x) = x^10 even, odd, or neither?

The function f(x) = x^10 is an even function because f(-x) = (-x)^10 = x^10 = f(x).

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Is f(x) = 16 - x - x^3 even, odd, or neither?

The function f(x) = 16 - x - x^3 is neither even nor odd because f(-x) = 16 + x + x^3 and neither this result nor its negative matches the original function.

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Is f(x) = -x^2 - x^4 even, odd, or neither?

The function f(x) = -x^2 - x^4 is an even function because f(-x) = -(-x)^2 - (-x)^4 = -x^2 - x^4 = f(x).

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Is f(x) = x^5 even, odd, or neither?

The function f(x) = x^5 is an odd function because f(-x) = (-x)^5 = -x^5 = -f(x).

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Is f(x) = -x^5 even, odd, or neither?

The function f(x) = -x^5 is also an odd function because f(-x) = -(-x)^5 = x^5 = -f(x).

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Is f(x) = 9 + x + x^2 even, odd, or neither?

The function f(x) = 9 + x + x^2 is neither even nor odd because f(-x) = 9 - x + x^2 and neither this result nor its negative matches the original function.

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Is f(x) = x^2 + x^6 + x^10 even, odd, or neither?

The function f(x) = x^2 + x^6 + x^10 is an even function because f(-x) = (-x)^2 + (-x)^6 + (-x)^10 = x^2 + x^6 + x^10 = f(x).

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Is f(x) = -x^2 - x^6 - x^10 even, odd, or neither?

The function f(x) = -x^2 - x^6 - x^10 is also an even function because f(-x) = -(-x)^2 - (-x)^6 - (-x)^10 = -x^2 - x^6 - x^10 = f(x).

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Is f(x) = sin(x) + 2 even, odd, or neither?

The function f(x) = sin(x) + 2 is neither even nor odd. It's odd because sin(-x) = -sin(x), but the constant term 2 prevents it from being a true odd function.

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Is f(x) = sin(x^2) even, odd, or neither?

The function f(x) = sin(x^2) is an even function because f(-x) = sin((-x)^2) = sin(x^2) = f(x).

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Is f(x) = sin(x^3) even, odd, or neither?

The function f(x) = sin(x^3) is an odd function because f(-x) = sin((-x)^3) = sin(-x^3) = -sin(x^3) = -f(x).

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Is f(x) = sin(-x) even, odd, or neither?

The function f(x) = sin(-x) is an odd function because f(-x) = sin(-(-x)) = sin(x) = -f(x).

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Is f(x) = sin(-x^2) even, odd, or neither?

The function f(x) = sin(-x^2) is an even function because f(-x) = sin(-(-x)^2) = sin(-x^2) = sin(x^2) = f(x).

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Is f(x) = sin(-x^3) even, odd, or neither?

The function f(x) = sin(-x^3) is an odd function because f(-x) = sin(-(-x^3)) = sin(x^3) = -f(x).

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Is f(x) = cos(x) + sin(x) - 3 even, odd, or neither?

The function f(x) = cos(x) + sin(x) - 3 is neither even nor odd. The cosine term is even, the sine term is odd, and the constant term is neither.

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Is f(x) = cos(-x) + x even, odd, or neither?

The function f(x) = cos(-x) + x is neither even nor odd. The cosine function is even, but the linear term is odd.

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Is f(x) = cos(x^2) even, odd, or neither?

The function f(x) = cos(x^2) is an even function because f(-x) = cos((-x)^2) = cos(x^2) = f(x).

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Is f(x) = cos(-x^2) even, odd, or neither?

The function f(x) = cos(-x^2) is also an even function because f(-x) = cos(-(-x)^2) = cos(-x^2) = cos(x^2) = f(x).

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Study Notes

Determining Even or Odd Functions

  • Even Function: A function is even if f(x) = f(-x) for all x in the domain. Graphically, an even function is symmetrical about the y-axis.
  • Odd Function: A function is odd if f(x) = -f(-x) for all x in the domain. Graphically, an odd function is symmetrical about the origin.
  • Neither: If a function does not satisfy either of the above conditions, it is neither even nor odd.

Examples of Functions

  • f(x) = x² + 5: Even, because f(x) = f(-x)
  • f(x) = x + 15: Odd, because f(x) = -f(-x)
  • f(x) = x⁷: Odd, because f(x) = -f(-x)
  • f(x) = x³ - 15: Odd, because f(x) = -f(-x)
  • f(x) = x² + x³ + 10: Neither
  • f(x) = x²: Even, because f(x) = f(-x)
  • f(x) = -x²: Even, because f(x) = f(-x)
  • f(x) = x³: Odd, because f(x) = -f(-x)
  • f(x) = -x³: Odd, because f(x) = -f(-x)
  • f(x) = x⁴ + x² + 5: Even, because f(x) = f(-x)
  • f(x) = x¹⁰: Even, because f(x) = f(-x)
  • f(x) = 16/x³: Neither
  • f(x) = x²- x²: Neither
  • f(x) = x⁵: Odd, because f(x) = -f(-x)
  • f(x) = -x⁵: Odd, because f(x) = -f(-x)
  • f(x) = 9 + x + x²: Neither
  • f(x) = x² + x⁶ + x¹⁰: Even, because f(x) = f(-x)
  • f(x) = -x² - x⁶ - x¹⁰: Odd, because f(x) = -f(-x)
  • f(x) = sin(x): Odd, because f(x) = -f(-x), sine is an odd function
  • f(x) = sin(x²): Neither
  • f(x) = cos(x²): Even, because cos(x²) = cos((-x)²)
  • f(x) = cos(-x²): Even, because cos(-x²) = cos(x²)
  • f(x) = cos(x) + sin(x³): Neither

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Related Documents

How to Tell If a Function is Even or Odd PDF

Description

This quiz focuses on identifying even and odd functions in mathematics. You will learn the definitions and properties of even and odd functions through examples and exercises. Test your understanding of these concepts to enhance your math skills.

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