Question

A fly starts out 2 meters from a lightbulb, flies closer to the light, then farther away (2
meters again). At this point the fly goes toward the bulb again, but hits the bulb and then
finally flies away.
A. Find a function (it may be piecewise) that gives the distance of the bug from the light as
a function of time. [There is more than one solution here—you have lots of freedom with
what your function can be, but it must satisfy the situational requirements given.]
Demonstrate that your function DOES satisfy the situational requirements.

B. What is the domain and range of your function for this situation?

Answer 1

because the fly is oscillating between two values, I'd choose a sinusoidal function. y = cos(x) oscillates between -1 and 1 so all we need to do is shift the position. suppose the lightbulb is 0. the fly starts out 2 meters from the lightbulb, so we can define that position as 2, and have the function go towards 0 and back towards 2. all we have to do is add 1 to the cos function to have it oscillate between 0 and 2 instead of -1 and 1.

the cos function repeats infinitely, but if we want to limit the domain to one cycle (starting at 2, going to 0, then going out to 2 again) we can find the period. by default the period of a cos function is 2pi. since we only shifted the function up, the period of our new function isn't affected, so it's still 2pi.

so we can define our function as y = cos(x) + 1 from x = 0 to x = 2pi, with range 0 - 2

to demonstrate that this function satisfies the requirements, you can graph it from x = 0 to x = 2pi