AP Precalculus Unit 1 Review

Front

What is a point of inflection?

Back

A point of inflection is where the rate of change of a function changes from increasing to decreasing or from decreasing to increasing.

Front

What does 'over equal-length interval' mean?

Back

It means the x-values are evenly spaced.

Front

If the graph of a function crosses the x-axis, what does that indicate about the multiplicity of that zero?

Back

It indicates that the multiplicity of that zero is odd.

Front

If x = a is a zero of a polynomial function p(x), what can be said about (x - a)?

Back

It is a linear factor of p.

Front

If a+bi is a root of a polynomial, what is also a root?

Back

a-bi is also a root.

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form p(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What does it mean for a polynomial to have a zero at x = a?

Back

It means that p(a) = 0, indicating that the graph of the polynomial touches or crosses the x-axis at that point.

Front

What is the relationship between the roots and factors of a polynomial?

Back

Each root of a polynomial corresponds to a factor of the form (x - r), where r is the root.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.