Exploring Polynomial Functions

This video provides an introduction to polynomial functions, explaining their standard form, how to identify them, and their key components such as degree and lead coefficient. It covers graphing techniques, focusing on the number of direction changes and end behavior based on the degree and lead coefficient. The video also demonstrates how to evaluate polynomial functions by substituting specific values.

What is the requirement for the exponents in a polynomial function?

• They can be any real number.

• They must be negative integers.

• They must be whole numbers.

• They must be fractions.

Which of the following is true about the coefficients in a polynomial function?

• They must be negative integers.

• They must be whole numbers.

• They can be any real number.

• They must be positive integers.

What is the term for the coefficient of the term with the largest exponent in a polynomial function?

• Variable

• Lead coefficient

• Constant

• Degree

How do you classify a polynomial function based on its largest exponent?

• By its variable

• By its constant term

• By its degree

• By its lead coefficient

What does the degree of a polynomial function indicate about its graph?

• The number of variables

• The number of coefficients

• The number of constants

• The number of direction changes

What is the end behavior of a polynomial function with an odd degree?

• The graph is always increasing.

• The graph points in opposite directions at both ends.

• The graph is always decreasing.

• The graph points in the same direction at both ends.

How does a positive lead coefficient affect the end behavior of a polynomial function?

• The graph points down as x approaches positive infinity.

• The graph points up as x approaches positive infinity.

• The graph points down as x approaches negative infinity.

• The graph points up as x approaches negative infinity.

What does the notation f(x) approaches positive infinity as x approaches positive infinity mean?

• Y is getting bigger as x is getting smaller.

• Y is getting smaller as x is getting smaller.

• Y is getting smaller as x is getting bigger.

• Y is getting bigger as x is getting bigger.

What is the first step in evaluating a polynomial function when given a specific value for x?

• Find the lead coefficient.

• Rewrite the polynomial in standard form.

• Substitute the given value for x.

• Simplify the polynomial.

If f(3) for a polynomial function equals 98, what does this tell you?

• The constant term is 98.

• The value of the function at x=3 is 98.

• The lead coefficient is 98.

• The degree of the polynomial is 3.