Rational Functions and Equations Quiz

A function that can be written as the ratio of two polynomials, where the denominator cannot be zero.

The horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

The vertical line that the graph of a function approaches as x approaches a certain value, where the denominator of the rational function becomes zero.

A point where the function is undefined, but the graph can be 'filled in' to make it continuous. The numerator and denominator of the rational function share a common factor, which makes the function undefined at that point.

A horizontal line that the graph of a function approaches as x approaches positive or negative infinity, when the degree of the numerator is one more than the degree of the denominator.

A value of x that makes the denominator of a rational function zero, resulting in a vertical asymptote or a hole.

The set of all possible input values (x-values) for which the function is defined.

The value of the function when x is equal to zero. Find by plugging in x=0 into the function.

The value(s) of x that make the function equal to zero. Find by setting the function equal to zero and solving for x.

A process used to solve an equation that involves rational expressions. It involves finding the least common multiple (LCM) of all denominators and then multiplying both sides of the equation by the LCM.

A solution obtained during the solving process of a rational equation that does not actually satisfy the original equation. It is a solution that is introduced by multiplying both sides of an equation by an expression that contains a variable, and that expression is equal to zero for that solution.

An inequality involving one or more rational expressions.

An inequality that involves one or more polynomial expressions.

A solution to a polynomial or rational inequality that makes the inequality true.

The set of solutions to an inequality, represented on a number line or in interval notation.

A method for solving polynomial and rational inequalities. It involves finding the critical points (where the expression equals zero or is undefined), dividing the number line into intervals, and testing a value in each interval to determine whether the inequality is true or false for that interval.

A value of x that makes the numerator or the denominator of a rational expression equal to zero.

The process of finding the roots (x-intercepts) of a polynomial equation. It involves factoring the polynomial, setting each factor equal to zero, and solving for x.

The highest power of the variable in a polynomial expression.

A polynomial with only one term.

A polynomial with two terms.

A polynomial with three terms.

An equation that involves rational expressions.

An expression that can be written as the ratio of two polynomials.