AP Precalculus Unit 1 Review

Front

What is an odd function?

Back

A function f(x) is considered odd if for every x in the domain, f(-x) = -f(x). This means the graph of the function is symmetric with respect to the origin.

Front

What does it mean if x = a is a zero of a polynomial function p(x)?

Back

If x = a is a zero of p(x), it means that p(a) = 0. This implies that (x - a) is a linear factor of the polynomial.

Front

How do you calculate the Average Rate of Change (ROC) between two points on a graph?

Back

The Average Rate of Change between two points (x1, y1) and (x2, y2) is calculated using the formula: Average ROC = (y2 - y1) / (x2 - x1), which represents the slope of the line connecting the two points.

Front

What is a root or zero of a polynomial function?

Back

A root or zero of a polynomial function p(x) is a value a such that p(a) = 0. It indicates where the graph of the polynomial intersects the x-axis.

Front

If a polynomial function has a degree n, what does that imply about its zeros?

Back

The degree n of a polynomial function indicates the maximum number of zeros (real or complex) it can have. For example, a polynomial of degree 5 can have up to 5 zeros.

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The degree of a polynomial determines its end behavior: if the degree is even, the ends of the graph will either both go up or both go down; if the degree is odd, one end will go up and the other will go down.

Front

What is the significance of complex zeros in polynomial functions?

Back

Complex zeros occur in conjugate pairs. If a polynomial has real coefficients and a complex zero, its conjugate must also be a zero.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function of degree n has exactly n roots in the complex number system, counting multiplicities.

Front

How can you determine the number of real zeros of a polynomial function?

Back

The number of real zeros can be determined using the Descartes' Rule of Signs, which provides a way to estimate the number of positive and negative real zeros based on the sign changes in the polynomial.

Front

What is the difference between a polynomial function and a rational 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 are constants and n is a non-negative integer. A rational function is a ratio of two polynomial functions.