1.3 Basic Functions - Ottawa Hills Local · PDF file 2017-10-04 · September 28,...

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  • September 28, 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)=x2 f(x)=x3

    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

  • September 28, 2009

    Find the domain of each basic function.

  • September 28, 2009

    Which of the functions have points of discontinuity?

  • September 28, 2009

    Which functions are bounded (above and below)?

  • September 28, 2009

    Which functions are even?

  • September 28, 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?

  • September 28, 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

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Identity

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Squaring

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Cubing

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Reciprocal

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Square Root

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Exponential

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Natural Logarithm

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Sine

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Cosine

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Absolute Value

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Greatest Integer

  • September 28, 2009

    Basic Function: ________________________

    Domain: ____________________________________

    Range: _____________________________________

    Continuity: __________________________________

    Increasing/Decreasing behavior: _________________

    Symmetry: __________________________________

    Boundedness: _______________________________

    Local Extrema: _______________________________

    Horizontal Asymptotes: ________________________

    Vertical Asymptotes: __________________________

    End behavior: ________________________________

    f(x) = _____________

    Logistic