Rational Functions

Questions and Answers

What is an asymptote?

A line that a graph approaches but does not reach (correct)

A type of polynomial function

A constant set of values

A point at which a graph is not connected

What is a rational function?

A function given by a fraction of polynomials where the denominator is not 0.

What is a hole on a graph?

A removable discontinuity that can be repaired by filling in a single point.

What does continuity refer to in graphing?

A connected graph without skipping any numbers or values. Signup and view all the answers

What is a discontinuity?

A point at which the graph of a relation or function is not connected. Signup and view all the answers

What is a removable discontinuity?

A hole in the graph. Signup and view all the answers

Study Notes

Asymptote

Represents a line that a graph approaches but never touches.
Can be classified into three types: vertical, horizontal, and slanted.

Rational Function

Defined as a function represented by a fraction where both the numerator and denominator are polynomials.
The general form is P(x)/Q(x), with the requirement that the denominator Q(x) is not equal to zero.

Hole (on a graph)

A specific type of discontinuity known as a removable discontinuity.
Occurs at points in a graph where there is a lack of connection but can be "fixed" by adding a single point.

Continuity

Characterizes a graph that is unbroken and connected.
Ensures that there are no gaps or skipped values within the set of numbers represented.

Discontinuity

Refers to points on a graph where the function or relation is not connected.
Discontinuities are classified as removable or essential, with essential discontinuities including step discontinuities (like step functions).

Removable Discontinuity

Identified as a hole within the graph where the function is continuous everywhere else except at that point.
Mathematically defined at x=c, indicating the graph can be made continuous by filling the hole at that point.

Description

Test your knowledge on rational functions with these flashcards. Learn key terms such as asymptotes, holes in graphs, and the definition of a rational function. Perfect for Algebra 2 students seeking to improve their understanding of the topic.