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)=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

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Page 1: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

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

Page 2: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Find the domain of each basic function.

Page 3: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Which of the functions have points of discontinuity?

Page 4: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Which functions are bounded (above and below)?

Page 5: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Which functions are even?

Page 6: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

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?

Page 7: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

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

Page 8: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Identity

Page 9: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Squaring

Page 10: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Cubing

Page 11: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Reciprocal

Page 12: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

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

Page 13: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Exponential

Page 14: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

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

Page 15: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Sine

Page 16: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Cosine

Page 17: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

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

Page 18: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

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

Page 19: 1.3 Basic Functions - Ottawa Hills Local School · PDF fileNatural Logarithm Fn Sine Fn Cosine Fn Absolute Value Fn Greatest Integer Fn Logistic Fn f(x)=x ... different function rule

September 29, 2009

Basic Function: ________________________

Domain: ____________________________________

Range: _____________________________________

Continuity: __________________________________

Increasing/Decreasing behavior: _________________

Symmetry: __________________________________

Boundedness: _______________________________

Local Extrema: _______________________________

Horizontal Asymptotes: ________________________

Vertical Asymptotes: __________________________

End behavior: ________________________________

f(x) = _____________

Logistic