Algebra 85 - Building Polynomial Functions

The video tutorial introduces polynomial functions, explaining their structure and how monomials form them. It discusses the impact of monomial coefficients on graph shapes, including vertical stretching, compressing, and reflecting. The tutorial explores how adding monomials affects polynomial graphs, focusing on end behavior and direction changes. By adding terms with different exponents, the video demonstrates how complex graphs with multiple direction changes are created. The tutorial concludes with a discussion on sketching polynomial graphs without digital tools.

What is the term with the largest exponent in a polynomial called?

• Middle term

• Leading term

• Constant term

• Final term

How does a negative coefficient affect the graph of a monomial?

• It shifts the graph upwards

• It reflects the graph across the X-axis

• It compresses the graph horizontally

• It stretches the graph vertically

What is the result of adding X^2 and X^4?

• A trinomial

• A binomial

• A monomial

• A constant

How can the end behavior of a polynomial function be predicted?

• By considering the smallest exponent

• By looking at the middle term

• By examining the leading term

• By analyzing the constant term

What happens to the graph of a polynomial when a term with a larger exponent is added?

• The graph remains unchanged

• The graph becomes simpler

• The graph's direction changes more frequently

• The graph's end behavior is dominated by the new term

What is the effect of reducing the coefficient of a term in a polynomial?

• It decreases the term's influence on the graph

• It increases the term's influence on the graph

• It has no effect on the graph

• It changes the term's exponent

What happens to the graph of a polynomial as X takes on very large values?

• It remains constant

• It follows the end behavior of the leading term

• It oscillates indefinitely

• It becomes a straight line

What is the effect of adding a term with a smaller coefficient to a polynomial?

• It allows each term to influence the graph over some range

• It makes the graph linear

• It eliminates all changes in direction

• It has no effect on the graph

What is the primary challenge in graphing polynomial functions without technology?

• Identifying the coefficients

• Determining the leading term

• Predicting the end behavior

• Sketching an accurate representation

What tool can be used to create accurate graphs of polynomial functions?

• A ruler

• A protractor

• A computer program

• A compass