Even and Odd Functions: Mastery Check

• Even

• Odd

• Neither

For the function \( g(x) = x^2 + 2 \), identify the type of symmetry it exhibits.

• Symmetric about the y-axis

• Symmetric about the x-axis

• Symmetric about the origin

• No symmetry

What is the domain of the function \( h(x) = \frac{1}{x^2 + 1} \)?

• All real numbers

• All real numbers except \( x = 0 \)

• All real numbers except \( x = 1 \)

• All real numbers except \( x = -1 \)

Find the range of the function \( f(x) = 2x^2 - 4 \).

• \( y \geq -4 \)

• \( y > -4 \)

• \( y \leq -4 \)

• \( y < -4 \)

If \( f(x) = x^5 - 2x^3 + x \), determine \( f(-x) \) and decide if the function is even, odd, or neither.

• \( f(-x) = -x^5 + 2x^3 - x \), Odd

• \( f(-x) = x^5 - 2x^3 + x \), Even

• \( f(-x) = -x^5 + 2x^3 - x \), Even

• \( f(-x) = x^5 - 2x^3 + x \), Neither

For the function \( g(x) = x^3 + 3 \), identify the type of symmetry it exhibits.

• Symmetric about the y-axis

• Symmetric about the x-axis

• Symmetric about the origin

• No symmetry

What is the range of the function \( f(x) = 3x^2 + 2 \)?

• \( y \geq 2 \)

• \( y > 2 \)

• \( y \leq 2 \)

• \( y < 2 \)

If \( f(x) = x^4 - 3x^2 + 2 \), determine \( f(-x) \) and decide if the function is even, odd, or neither.

• \( f(-x) = -x^4 + 3x^2 - 2 \), Odd

• \( f(-x) = x^4 - 3x^2 + 2 \), Even

• \( f(-x) = -x^4 + 3x^2 - 2 \), Even

• \( f(-x) = x^4 - 3x^2 + 2 \), Neither

For the function \( h(x) = x^4 + 4 \), identify the type of symmetry it exhibits.

• Symmetric about the y-axis

• Symmetric about the x-axis

• Symmetric about the origin

• No symmetry

If \( f(x) = x^6 - 3x^4 + 2x^2 \), determine \( f(-x) \) and decide if the function is even, odd, or neither.

• \( f(-x) = -x^6 + 3x^4 - 2x^2 \), Odd

• \( f(-x) = x^6 - 3x^4 + 2x^2 \), Even

• \( f(-x) = -x^6 + 3x^4 - 2x^2 \), Even

• \( f(-x) = x^6 - 3x^4 + 2x^2 \), Neither