For drawing on the Smiley Face I started by making the eyebrows with the square root function. I shifted the function up by adding values to the sqrt; shifted horizontally by adding to the value under the root; and reflected over the y axis by negating the x value under the sqrt. Restricted domain since eyebrows are not infinite.
The mustache was made by the cos function. The period was adjusted by changing the multiplier on the input for the cos function. The amplitude was flattened out by multiplying the cos value by .5. The function was moved vertically by subtracting from the output. The domain was restricted to allow a curl on the mustache.
The beard is the absolute value function; multiplied by 4 to narrow (stretch) the function; and subtracted 6 from the function to move it down into place. Domain was restricted to stop the drawing.
Ears are four linear functions. Domains were restricted to attach at head and create the point of the ears.
The hair is a cubic function. The input value was decreased by 1 to shift the graph to right by 1; the function value was increased by 5 to move the graph up. The domain was restricted to begin the hair on the circle, and have finite length of the hair strand.
The mustache was made by the cos function. The period was adjusted by changing the multiplier on the input for the cos function. The amplitude was flattened out by multiplying the cos value by .5. The function was moved vertically by subtracting from the output. The domain was restricted to allow a curl on the mustache.
The beard is the absolute value function; multiplied by 4 to narrow (stretch) the function; and subtracted 6 from the function to move it down into place. Domain was restricted to stop the drawing.
Ears are four linear functions. Domains were restricted to attach at head and create the point of the ears.
The hair is a cubic function. The input value was decreased by 1 to shift the graph to right by 1; the function value was increased by 5 to move the graph up. The domain was restricted to begin the hair on the circle, and have finite length of the hair strand.