A Library of Graphed Functions

(To view, click on the Thumbnails below)

Group 1:  Polynomials: 

        Constant:    

        Linear:                  

        Quadratic:                  

        Cubic:                            

        Quartic:                            

        A sequence of even polynomials, degree 2n, which approaches cos(x) as n gets large:

        A sequence of odd polynomials, degree 2n + 1, which approaches sin(x) as n gets large:

Group 2: Trigonometric Functions

        A sin(Bx - C) + D with Amplitude A, Frequency B, Phase Shift C, and Vertical Shift D

        A cos(Bx - C) + D with Amplitude A, Frequency B, Phase Shift C, and Vertical Shift D

        tan, cot, sec, csc with Amplitude A, Frequency B, Phase Shift C, and Vertical Shift D

Group 3:  Exponential Functions

Group 4:  Logarithmic Functions

Group 5:  Rational Functions

Group 6:  Relations which are NOT functions:

Group 7:  Pairs of Inverse functions:

Group 8:  3-dimensional functions, z = f(x, y):

                 arranged as i) from arbitrary angle, ii) from one coordinate axis,

                 iii) from the other coordinate axis, iv) the contour map from above:

              Function 1:            

              Function 2:            

              Function 3:            

Group 9:  Functional Building Blocks

   a) x to the power of an even positive integer:  0, 2, 4, 6, 10, 100

   b) x to the power of an odd positive integer:  1, 3, 5, 7, 11, 101

   c) x to the power of an even negative integer:  -2, -4, -6, -8, -16, -100

   d) x to the power of an odd negative integer:  -1, -3, -5, -7, -15, -99

   e) x to the power of 1 / "an even positive integer":   1/2, 1/4, 1/6, 1/10, 1/100

   f) x to the power of 1 / "an odd positive integer":   1/3, 1/5, 1/7, 1/11, 1/101

Group 10:  Transformations of a function:

        a) Translate, or Shift,  f(x) left, right, up, or down:

        b) Reflect across the horizontal or vertical axis:

     c) Dilation/Contraction in the horizontal and vertical directions

    d) Several Consecutive Transformations...

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