Exploring Even and Odd Polynomial Functions

The video tutorial covers section 1.5, focusing on even and odd polynomials. It begins with feedback from previous lessons and promises a concise session. The tutorial explains even functions as symmetrical over the y-axis and odd functions as symmetrical over the origin. It provides rules for identifying these functions and demonstrates how to prove them algebraically. The video includes examples and practice problems to determine if functions are even, odd, or neither, emphasizing the importance of checking symmetry rather than relying solely on polynomial degree.

What is the main characteristic of even functions?

• They are symmetrical over the y-axis.

• They are symmetrical over the origin.

• They are symmetrical over the x-axis.

• They have no symmetry.

Which of the following is true for an even function f(x)?

• f(x) = -f(x)

• f(x) = f(-x)

• f(x) = -f(-x)

• f(x) = x

How can you prove a function is even algebraically?

• Substitute x with -x and see if you get -x.

• Substitute x with -x and see if you get x.

• Substitute x with -x and see if you get -f(x).

• Substitute x with -x and see if you get f(x).

What does it mean for a function to be symmetrical over the origin?

• It is symmetrical over the y-axis.

• It has no symmetry.

• It is symmetrical over the x-axis.

• It is symmetrical over the point (0,0).

Which of the following is true for an odd function f(x)?

• f(x) = x

• f(x) = -f(x)

• f(x) = f(-x)

• f(x) = -f(-x)

How can you prove a function is odd algebraically?

• Substitute x with -x and see if you get f(x).

• Substitute x with -x and see if you get -f(x).

• Substitute x with -x and see if you get -x.

• Substitute x with -x and see if you get x.

What is the result of substituting -x into the function f(x) = 6x^4 - 2x?

• 6x^4 - 2x

• -6x^4 + 2x

• 6x^4 + 2x

• -6x^4 - 2x

If a polynomial has an even degree, what can we infer about its symmetry?

• It might be an odd function.

• It might be an even function.

• It is always an odd function.

• It is always an even function.

What is the rule for determining if a simple polynomial function with one term is even or odd?

• Check if the function is symmetrical over the y-axis.

• Check if the function is symmetrical over the x-axis.

• Check if the exponent is even or odd.

• Check if the coefficient is positive or negative.

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

• Look at the degree of the polynomial.

• All of the above.

• Check the symmetry of the function.

• Substitute x with -x and simplify.