APPC 1-4 Polynomial Functions & ROC Vocab

Choose the most accurate definition or description for the term Nonconstant Polynomial Function.

• A function of degree zero

• A function equivalent to p(x)=anxn+⋯+a1x+a0 with an≠0 and n>0

• A function with only constant terms

• A function with no zeros

Choose the most accurate definition or description for the term Degree of a Polynomial.

• The highest power of x with a nonzero coefficient

• The sum of all powers of x

• The number of terms in the polynomial

• The coefficient of the constant term

Choose the most accurate definition or description for the term Leading Coefficient.

• The coefficient of the constant term

• The coefficient of the highest degree term an

• The degree of the polynomial

• The value of p(0)

Choose the most accurate definition or description for the term Local Maximum.

• The greatest function value over the entire domain

• A function value greater than all values in some neighborhood around the input

• A point where the function is increasing

• A zero of the polynomial

Choose the most accurate definition or description for the term Global Minimum.

• The least of all local minima or the smallest function value over the entire domain

• A point where the function changes from decreasing to increasing

• The zero with the smallest input value

• The degree of the polynomial

Choose the most accurate definition or description for the term Relationship Between Zeros and Local Extrema.

• Between every two distinct zeros, there must be at least one local maximum or minimum

• A polynomial has no local extrema between zeros

• Zeros occur only at local maxima

• Local maxima and minima only occur at zeros

Choose the most accurate definition or description for the term Global Behavior of Even-Degree Polynomials.

• They always have a global maximum only

• They will have either a global maximum or a global minimum

• They never have local extrema

• They have no inflection points

Choose the most accurate definition or description for the term Point of Inflection.

• Input values where the function value is zero

• Points where the concavity of the graph changes from up to down or down to up

• The highest degree term of the polynomial

• Points where the function is increasing

Choose the most accurate definition or description for the term Concavity Change in Polynomials.

• Occurs only at zeros of the polynomial

• Occurs at points of inflection where the second derivative changes sign

• Happens when the leading coefficient is zero

• Does not occur in polynomial functions

Choose the most accurate definition or description for the term Constant Polynomial Function.

• A polynomial of degree zero

• A polynomial with degree greater than zero

• A polynomial with only zeros as inputs

• A polynomial with no leading term