2 Review Polynomials and Rational Functions

Front

What are the zeros of the polynomial function f(x) = x^3(x + 1)^2(x - 4)?

Back

The zeros are 0 (multiplicity 3), -1 (multiplicity 2), and 4 (multiplicity 1).

Front

How do you factor the polynomial f(x) = x^3 - 9x?

Back

The factored form is f(x) = x(x - 3)(x + 3), with zeros at x = 0, 3, and -3.

Front

What is a vertical asymptote in rational functions?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

Given f(x) = 2x and g(x) = 2x^2 - 1, find f(g(x)).

Back

f(g(x)) = 4x^2 - 2.

Front

What are the decreasing intervals of a function?

Back

The decreasing intervals are the ranges of x where the function's output decreases as x increases.

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(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.

Front

What is the degree of a polynomial?

Back

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

Front

What does it mean for a zero to have multiplicity?

Back

Multiplicity refers to the number of times a particular zero appears as a root of the polynomial.

Front

How do you find the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be found by comparing the degrees of the numerator and denominator.

Front

What is the factored form of a polynomial?

Back

The factored form expresses the polynomial as a product of its linear factors.