Comparing Polynomial Functions: Determining Which Function Exceeds the Other

The video tutorial explains how to determine which of two polynomial functions eventually exceeds the other by comparing their degrees. It highlights the importance of the leading term in determining end behavior as x approaches infinity. Through visual examples and graphical analysis, it demonstrates that a polynomial with a higher degree will eventually surpass one with a lower degree, despite temporary leads by the latter. The tutorial concludes that the degree of the polynomial is the key factor in long-term dominance.

What is the primary factor in determining which polynomial function will eventually exceed the other?

• The constant term

• The number of terms in the polynomial

• The leading coefficient

• The degree of the polynomial

When comparing two polynomial functions, why can the leading term be used to determine which function will eventually exceed the other?

• Because the leading term has the smallest coefficient

• Because the leading term dominates as x approaches infinity

• Because the leading term is the first term in the equation

• Because the leading term is always the largest term

In the example comparing y = x^4 and y = 8x^3, at what value of x does x^4 begin to exceed 8x^3?

• x = 12

• x = 8

• x = 5

• x = 10

Why does x^4 eventually exceed 8x^3 as x increases?

• Because 8x^3 has fewer terms

• Because x^4 has a higher leading coefficient

• Because x^4 has a higher degree

• Because 8x^3 has a lower constant term

What general rule can be concluded about polynomial functions with different degrees?

• A polynomial with a lower degree will always exceed one with a higher degree

• Polynomials with the same degree will always have the same end behavior

• The coefficients of the polynomials determine which will exceed the other

• A polynomial with a higher degree will eventually exceed one with a lower degree

Which type of polynomial will eventually exceed a linear polynomial as x approaches infinity?

• A monomial with a lower degree

• A constant polynomial

• A quadratic polynomial

• A linear polynomial

What should be ignored when determining which polynomial function will eventually exceed the other?

• The degree of the polynomial

• The leading term

• The coefficients

• The number of variables