Even and Odd Functions Explained

The video tutorial explores the concepts of even and odd functions, explaining their origins and differences from even and odd degree polynomials. It highlights the graphical characteristics of even functions, such as symmetry over the y-axis, and odd functions, which exhibit origin point symmetry. The tutorial also provides methods to identify these functions using function notation and examples, including non-polynomial functions like cosine and sine.

What is the main difference between an even function and an even degree polynomial?

• An even degree polynomial must have an odd leading term.

• An even function must have symmetry over the x-axis.

• An even degree polynomial must have all even powers of x.

• An even function must be a polynomial.

Which of the following is a characteristic of an even function?

• It has symmetry over the y-axis.

• It has all odd powers of x.

• It has symmetry over the x-axis.

• It passes through the origin.

Which of the following is an example of an even function?

• tan(x)

• cos(x)

• sin(x)

• x^3 + x

What is the defining graphical characteristic of an even function?

• Symmetry over the x-axis

• Symmetry over the y-axis

• Symmetry around the origin

• No symmetry

What is the main characteristic of an odd function?

• Symmetry over the y-axis

• Symmetry around the origin

• Symmetry over the x-axis

• No symmetry

Which of the following is an example of an odd function?

• cos(x)

• x^2 + 1

• x^3 - x

• x^4 + x^2

What type of symmetry does an odd function exhibit?

• Symmetry over the x-axis

• Symmetry over the y-axis

• No symmetry

• Symmetry around the origin

Which of the following is true for all odd functions?

• They are always polynomials.

• They have all odd powers of x.

• They have all even powers of x.

• They have symmetry over the y-axis.

Which non-polynomial function is an example of an odd function?

• x^4

• x^2

• tan(x)

• cos(x)

What is the function notation for an even function?

• f(x) = -f(x)

• f(-x) = f(x)

• f(-x) = -f(x)

• f(x) = f(-x)