1.3 Basic FunctionsHow does the graph relate to any of the 12 basic functions? September 16, 2011...
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September 16, 2011 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)=x 2 f(x)=x 3 f(x)= 1 x f(x) = √x f(x) = e x f(x) = ln x f(x) = sin x f(x) = cos x f(x) = x f(x) = int (x) f(x) = 1 1 + e -x
Transcript of 1.3 Basic FunctionsHow does the graph relate to any of the 12 basic functions? September 16, 2011...
September 16, 2011
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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Find the domain of each basic function.
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Which of the functions have points of discontinuity?
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Which functions are bounded (above and below)?
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Which functions are even?
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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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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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Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Identity
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Squaring
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Cubing
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Reciprocal
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Square Root
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Exponential
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Natural Logarithm
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Sine
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Cosine
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Absolute Value
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Greatest Integer
September 16, 2011
Basic Function: ________________________
Domain: ____________________________________
Range: _____________________________________
Continuity: __________________________________
Increasing/Decreasing behavior: _________________
Symmetry: __________________________________
Boundedness: _______________________________
Local Extrema: _______________________________
Horizontal Asymptotes: ________________________
Vertical Asymptotes: __________________________
End behavior: ________________________________
f(x) = _____________
Logistic
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