PRE CALC FINAL

Give a clear and precise mathematical definition of a function.

a relationship between inputs where each input corresponds to exactly one output.

Compare and contrast the graphs of the sine and cosine function.

The sine and cosine functions have identical shapes, but differ in their starting points and phase shift. The sine function starts at zero, while the cosine function starts at a maximum value of 1

Give an every-day example in which you have applied or will apply your new mathematical learning in your art area.

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Reflect on your learning experience throughout this course and explain how you can use this to inform your performance next year for your new math course.

Reflecting on my experience, this class taught me the importance of discipline and practice. To improve my performance on any subject, it’s vital that I implement what is learned outside of school in practice problems and be committed to dedicating some of my time to it.

Explain how a, b, c, and d individually impact the graph of the cosine function.

Given the standard equation

y = aCos(bx+c) +d

the absolute value of a represents the amplitude, which is maximum distance the graph extends from the midline.

b represents the period and determines how many cycles a of the cosine function fit in a given interval

both a and b affect the shape of the function

c represents the phase shift and causes a horizontal shift in the graph

d represents a vertical shift in the graph

c and d affect the position of the function on graph