Lesson

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Aaron Thomas
Jacob Wefel
Tyler Sneen
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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
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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
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Domain: All Real Numbers
Range: All Real Numbers
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Domain: x> -1
Range: x>-5
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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
Jump Discontinuity
Removable Discontinuity
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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”
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This sine function is bounded above and
below at 1 and -1
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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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Local Min: 3, -4, 4
Local Max: 5
Absolute Max: None (Graph goes infinitely
upward)
Absolute Min: -4
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A horizontal asymptote is a part of the
function which gets infinitely close to a Yvalue 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
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
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