AP Precalculus 1.4-1.5

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) equals zero. It is also known as a root of the function.

Front

How do you determine if a number is a zero of a polynomial function?

Back

To determine if a number is a zero of a polynomial function, substitute the number into the function. If the result is zero, then it is a zero of the function.

Front

What does it mean for a function to be even?

Back

A function is even if f(-x) = f(x) for all x in the domain of the function. This means the graph of the function is symmetric about the y-axis.

Front

What does it mean for a function to be odd?

Back

A function is odd if f(-x) = -f(x) for all x in the domain of the function. This means the graph of the function is symmetric about the origin.

Front

What is the difference between a factor and a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero, while a factor is a polynomial that divides the original polynomial without leaving a remainder.

Front

How can you find the intervals where a polynomial function is negative?

Back

To find the intervals where a polynomial function is negative, determine the zeros of the function, then test the sign of the function in the intervals created by these zeros.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial. It determines the number of zeros and the end behavior of the graph.

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or zero) of a polynomial equation with integer coefficients is of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

What is a multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero appears as a root of the polynomial. A zero with an even multiplicity will touch the x-axis, while a zero with an odd multiplicity will cross the x-axis.

Front

How do you determine if a polynomial function is increasing or decreasing?

Back

To determine if a polynomial function is increasing or decreasing, analyze the first derivative of the function. If the derivative is positive, the function is increasing; if negative, it is decreasing.