graphs of logarithmic functions
DESCRIPTION
Graphs of Logarithmic Functions. One more fun day in Section 3.3 b. Let’s start with Analysis of the Natural Logarithmic Function:. The graph:. Domain:. Range:. Continuous on. Increasing on. No Symmetry. Unbounded. No Local Extrema. No Horizontal Asymptotes. Vertical Asymptote:. - PowerPoint PPT PresentationTRANSCRIPT
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Graphs of Logarithmic Functions
One more fun day in Section 3.3b
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Let’s start with Analysis of the Natural Logarithmic Function:Let’s start with Analysis of the Natural Logarithmic Function:
The graph: lnf x x
Domain: 0, Range: , Continuous on 0,Increasing on 0,
No Symmetry Unbounded
No Local Extrema No Horizontal Asymptotes
Vertical Asymptote: 0x
End Behavior: lim lnx
x
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The “Do Now” The “Do Now” Analysis of the Natural Logarithmic Function Analysis of the Natural Logarithmic Function
The graph: lnf x xNote: Any other logarithmicNote: Any other logarithmicfunctionfunction logbg x xwith with bb > 1 has the same domain, > 1 has the same domain,range, continuity, inc. behavior,range, continuity, inc. behavior,lack of symmetry, and otherlack of symmetry, and othergeneral behavior of the naturalgeneral behavior of the naturallogarithmic function!!!logarithmic function!!!
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Describe how to transform the graph of y = ln(x) or y = log(x)into the graph of the given function. Sketch the graph by handand support your answer with a grapher.
1. ln 2g x x Trans. left 2 Trans. left 2 The graph? The graph?
2. ln 3h x x Reflect across the Reflect across the yy-axis,-axis,Trans. right 3 Trans. right 3 The graph? The graph?
ln 3x
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Describe how to transform the graph of y = ln(x) or y = log(x)into the graph of the given function. Sketch the graph by handand support your answer with a grapher.
3. 3logg x xVert. stretch by 3 Vert. stretch by 3 The graph? The graph?
4. 1 logh x x Trans. up 1 Trans. up 1 The graph? The graph?
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Describe how to transform the graph of y = ln(x) or y = log(x)into the graph of the given function. Sketch the graph by handand support your answer with a grapher.
5. 2ln 2 2 3g x x
Trans. right 1, Horizon. shrink by 1/2,Trans. right 1, Horizon. shrink by 1/2,Reflect across both axes, Vert. stretch by 2,Reflect across both axes, Vert. stretch by 2,Trans. up 3 Trans. up 3 The graph??? The graph???
2ln 2 1 3x
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Graph the given function, then analyze it for domain, range,continuity, increasing or decreasing behavior, boundedness,extrema, symmetry, asymptotes, and end behavior.
1. log 2f x x D: 2, R: ,
Continuous Dec: 2, No Symmetry Unbounded No Local Extrema
Asy: 2x E.B.: limx
f x
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Graph the given function, then analyze it for domain, range,continuity, increasing or decreasing behavior, boundedness,extrema, symmetry, asymptotes, and end behavior.
2. 5ln 2 3f x x
D: , 2 R: ,
Continuous Dec: , 2 No Symmetry Unbounded No Local Extrema
Asy: 2x E.B.: limx
f x