Exploring Even and Odd Functions

What is the symmetry property of an even function?

• Symmetry across the line y = x

• Symmetry across the origin

• Symmetry across the y-axis

• Symmetry across the x-axis

Which of the following is true for an odd function?

• f(x) = -f(-x)

• f(-x) = f(x)

• f(x) = f(-x)

• f(-x) = -f(x)

What does the property f(-x) = f(x) indicate?

• The function is undefined

• The function is neither even nor odd

• The function is odd

• The function is even

In the example given, what is the result of substituting -x into the function f(x) = -3x^2 + 2?

• 3x^2 - 2

• -3x^2 - 2

• 3x^2 + 2

• -3x^2 + 2

What is the symmetry property of the function f(x) = -3x^2 + 2?

• Even

• Neither

• Odd

• Both

What is the result of substituting -x into the function g(x) = -x^3 - 5x?

• -x^3 - 5x

• -x^3 + 5x

• x^3 - 5x

• x^3 + 5x

What is the symmetry property of the function g(x) = -x^3 - 5x?

• Neither

• Even

• Odd

• Both

What is the result of substituting -x into the function h(x) = -x - 5?

• x - 5

• x + 5

• -x - 5

• -x + 5

What is the symmetry property of the function h(x) = -x - 5?

• Both

• Neither

• Odd

• Even

Which of the following functions is neither even nor odd?

• f(x) = x^2

• g(x) = x^3

• h(x) = -x - 5

• f(x) = x^4