If I Could Only Hear That Transformation*
Consider the function y = f(x) where f(1) = 3, f(2) = 5, f(3) = 2, f(4) = 4, f(5) = 3, f(6) = 0, and
f(7) = 1. Plot the ordered pairs (x, f(x)) for x = 1, 2, 3, . . . , 7 on the grid on the next page.
The graph of y = f(x) can be obtained by connecting consecutive ordered pairs with straight
line segments.
Now graph each of the following functions on the same grid in a different color. Be sure to
label each of your graphs.
(A) y = f(x) +2
(B) y = 2f(x)
(C) y = 2f(x) + 4
(D) y = - f(x)
As we listen to these transformations, fill in the table below:
Transformation
Observation in terms of graph and melody
y = f(x)+2
y = 2f(x)
y = 2f(x)+4
y = - f(x)
*Functional Melodies; Finding Mathematical Relationships in Music by Scott Beall. Key
Curriculum Press Copyright 2000.