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Questions and Answers
What is an asymptote?
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?
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?
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?
What does continuity refer to in graphing?
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What is a discontinuity?
What is a discontinuity?
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What is a removable discontinuity?
What is a removable discontinuity?
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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.
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