Understanding Even, Odd, and Neither Functions

What is the graphical representation of an even function?

• A 180-degree rotation about the origin

• A 90-degree rotation about the origin

• A reflection over the y-axis

• A reflection over the x-axis

How can you algebraically determine if a function is even?

• Replace x with -x and check if the function is multiplied by -1

• Replace x with -x and check if the function remains unchanged

• Replace x with x^2 and simplify

• Replace x with x^3 and simplify

What is the graphical representation of an odd function?

• A reflection over the x-axis

• A reflection over the y-axis

• A 90-degree rotation about the origin

• A 180-degree rotation about the origin

How can you algebraically determine if a function is odd?

• Replace x with -x and check if the function remains unchanged

• Replace x with -x and check if the function is multiplied by -1

• Replace x with x^2 and simplify

• Replace x with x^3 and simplify

What does it mean if a function is neither even nor odd?

• The function is a reflection over the y-axis

• The function does not satisfy the conditions for being even or odd

• The function is a 90-degree rotation about the origin

• The function is a reflection over the x-axis

In the example of f(x) = x^4 - 4x^2 + 1, what type of function is it?

• Both even and odd

• Neither

• Even

• Odd

For the function f(x) = x^5 - 7x, what type of function is it?

• Neither

• Both even and odd

• Odd

• Even

What is the result of replacing x with -x in the function f(x) = x^4/5?

• The function becomes negative

• The function becomes zero

• The function remains unchanged

• The function is multiplied by -1

In the function f(x) = x^5 - 2, why is it neither even nor odd?

• Because it is a reflection over the y-axis

• Because it is a reflection over the x-axis

• Because it does not satisfy the conditions for even or odd functions

• Because it has both even and odd powers

What should you do to verify if a function is even or odd?

• Replace x with x^4

• Graph it on a graphing calculator

• Replace x with x^2

• Replace x with x^3