1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine...
Transcript of 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine...
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September 29, 2009
1.3 Basic Functions
Identity Fn Squaring Fn Cubing Fn
Reciprocal Fn Square Root Fn Exponential Fn
Natural Logarithm Fn Sine Fn Cosine Fn
Absolute Value Fn Greatest Integer Fn Logistic Fn
f(x)=x f(x)=x2f(x)=x3
f(x)= 1x
f(x) = √x f(x) = ex
f(x) = ln xf(x) = sin x
f(x) = cos x
f(x) = x f(x) = int (x)
f(x) = 1
1 + e-x
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September 29, 2009
Find the domain of each basic function.
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September 29, 2009
Which of the functions have points of discontinuity?
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September 29, 2009
Which functions are bounded (above and below)?
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September 29, 2009
Which functions are even?
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September 29, 2009
Graph the function: f(x) = sin (x) + 5
a. On what interval, if any, is the function increasing? decreasing?
b. Is the function odd, even, or neither?
c. Give the function's extrema, if any.
d. How does the graph relate to any of the 12 basic functions?
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September 29, 2009
Piecewise Function: a function whose domain is divided into several parts and a different function rule is applied to each part.
f(x) = x2 if x ≤0 √x if x >0
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Identity
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Squaring
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Cubing
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Reciprocal
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Square Root
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Exponential
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Natural Logarithm
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Sine
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Cosine
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Absolute Value
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Greatest Integer
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September 29, 2009
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Logistic