Odd and Even Functions

Is the graph an even, odd, or neither function
                        f(x) = 4x³ 

• Even

• Odd

• Neither

Answer explanation

The function f(x) = 4x^3 is odd because f(-x) = -f(x). This means the graph is symmetric about the origin, confirming it is an odd function.

Is the graph an even, odd, or neither function
                        f(x) = x² + 2

• Even 

• Odd

• Neither

Answer explanation

The function f(x) = x² + 2 is even because f(-x) = (-x)² + 2 = x² + 2 = f(x). An even function satisfies the condition f(-x) = f(x) for all x.

Is the graph an even, odd, or neither function?

• Even

• Odd

• Neither

Answer explanation

The graph is an even function because it satisfies the condition f(x) = f(-x) for all x in its domain. This symmetry about the y-axis confirms that the correct choice is 'Even'.

Which one of the following functions is odd?

• f(x) = 3x⁴ - 4x³

• g(x) = 5x⁴ + 3x²

• h(x) = 6x⁵ - x³

• k(x) = x⁶ + 8x²

Answer explanation

An odd function satisfies f(-x) = -f(x). For h(x) = 6x⁵ - x³, h(-x) = -6x⁵ + x³ = -h(x). The other functions are even or neither, making h(x) the only odd function.

Even, odd, or neither?

• Even

• Odd

• Neither

• Please explain this to me.

Answer explanation

The number in question is classified as odd because it cannot be evenly divided by 2, resulting in a remainder. Therefore, the correct answer is 'Odd'.

• Even

• Odd

• Neither

Answer explanation

The function f(x) = 4x^2 + 8 is even because f(-x) = 4(-x)^2 + 8 = 4x^2 + 8 = f(x). An even function satisfies the condition f(-x) = f(x) for all x.

• Even

• Odd

• Neither

Answer explanation

The function f(x) = 2x^3 is classified as odd because f(-x) = -f(x). This means that the function is symmetric about the origin, confirming it is an odd function.

• Even

• Odd

• Neither

Answer explanation

The function f(x) = -x^2 is even because f(-x) = -(-x)^2 = -x^2 = f(x). An even function satisfies the condition f(-x) = f(x) for all x.

Is the graph an even, odd, or neither function?

• Even

• Odd

• Neither

Answer explanation

The graph is an even function because it satisfies the condition f(x) = f(-x) for all x in its domain. This symmetry about the y-axis confirms that the correct choice is 'Even'.

Which one of the following functions is even?

• f(x) = x⁴ + x³

• g(x) = x⁴ + x²

• h(x) = x⁵ + x³

• k(x) = x³ + x

Answer explanation

An even function satisfies f(-x) = f(x). For g(x) = x⁴ + x², g(-x) = (-x)⁴ + (-x)² = x⁴ + x² = g(x). Thus, g(x) is even. The other functions do not satisfy this property.