Final answer:
To create a sine function with an amplitude of 3 and a vertical shift of 6, the equation is y(x) = 3*sin(x) + 6. This function will oscillate between +9 and +3.
Step-by-step explanation:
To create a sine function with an amplitude of 3 and a vertical shift up 6, we follow standard sine function transformations. A sine function generally oscillates between +1 and -1, and has a period of 2π radians.
When the amplitude is increased, the peak and trough of the wave are multiplied by this factor, and setting a vertical shift moves the entire function up or down on the graph.
Based on the given information, the sine function equation will be:
y(x) = 3*sin(x) + 6
Here, '3' represents the amplitude, meaning that the sine wave will oscillate between +3 and -3, and then we add 6 to shift the entire wave up, resulting in a wave that oscillates between +9 and +3.