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Transcript of Aaron Thomas Jacob Wefel Tyler Sneen. By the end of this lesson we will introduce the terminology...
![Page 1: Aaron Thomas Jacob Wefel Tyler Sneen. By the end of this lesson we will introduce the terminology that is used to describe functions These include:](https://reader037.fdocuments.in/reader037/viewer/2022103123/56649db95503460f94aa99d5/html5/thumbnails/1.jpg)
Section 1.2 Functions and their Properties
Aaron ThomasJacob WefelTyler Sneen
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Funny Introduction
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Introduction
By the end of this lesson we will introduce the terminology that is used to describe functions
These include: Domain, Range, Continuity, Discontinuity, upper and lower bound, Local and absolute maximums and minimums, and asymptotes
![Page 4: Aaron Thomas Jacob Wefel Tyler Sneen. By the end of this lesson we will introduce the terminology that is used to describe functions These include:](https://reader037.fdocuments.in/reader037/viewer/2022103123/56649db95503460f94aa99d5/html5/thumbnails/4.jpg)
Domain and Range
The domain of a function is all of the possible x-values the function can have. It can be expressed as an inequality
The Range of a function is all of the possible y-values the function can have. It is also expressed as an inequality
![Page 5: Aaron Thomas Jacob Wefel Tyler Sneen. By the end of this lesson we will introduce the terminology that is used to describe functions These include:](https://reader037.fdocuments.in/reader037/viewer/2022103123/56649db95503460f94aa99d5/html5/thumbnails/5.jpg)
Domain and Range Example
Domain: All Real Numbers Range: All Real Numbers
Domain: x> -1 Range: x>-5
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Discontinuity
A graph has continuity if its graph is connected to itself throughout infinity. There are no asymptotes or holes in the graph
A Graph has removable discontinuity if its graph has a hole where one x value was removed from the domain
A graph has infinite discontinuity if its graph has an asymptote that can not be replaced with only one value
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Discontinuity Example
Jump Discontinuity Removable Discontinuity
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Bindings
A function is bounded above or below if the graph’s range doesn’t extend past a certain point above or below.
A function is “Bounded” if the function’s range doesn’t extend below or above certain points
If the function has no restrictions on its range’s extent the function is considered “unbounded”
![Page 9: Aaron Thomas Jacob Wefel Tyler Sneen. By the end of this lesson we will introduce the terminology that is used to describe functions These include:](https://reader037.fdocuments.in/reader037/viewer/2022103123/56649db95503460f94aa99d5/html5/thumbnails/9.jpg)
Bindings Example
This sine function is bounded above and below at 1 and -1
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Max and Mins
A Local Maximum/Minimum of a function is the highest/lowest point of the range in the surrounding window of the graph
The absolute maximum/minimum of a function is the highest/lowest point of the entire range of the graph
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Max and Min Example
Local Min: 3, -4, 4 Local Max: 5 Absolute Max: None (Graph goes
infinitely upward) Absolute Min: -4
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Asymptotes
A horizontal asymptote is a part of the function which gets infinitely close to a Y-value but never touches it
A Vertical asymptote is a part of the function which gets infinitely close to a x- value but never touches it
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Asymptotes Example
Identify any horizontal or vertical asymptotes of the graph of
You would first start by foiling the denominator… = (x+1)(x-2)
This means that the graph has vertical asymptotes of x=-1 and x=2
Because the denominator’s power is bigger than the numerator’s, y = 0 no matter what the value of x is
Now you have x/((x+1)(x-2)) = 0 This means that the horizontal asymptote is
zero