EMT 668
Final Project V
by
Beth Richichi

Let f(x)=a sin(bx+c) and g(x)=a cos(bx+c). For selected values of a, b, and c, graph and explore:

i. h(x) = f(x) + g(x)
ii. h(x) = f(x) * g(x)
iii. h(x) =f(x) / g(x)
iv. h(x) = f(g(x))

First let's examine the following graphs where a, b, and c have values of one. The red graph has the equation f(x) = sin(x+1). The green graph has the equation g(x)=cos(x+1).

Let's examine the results when we perform operations on the two functions:

When a and b have positive values and c is equal to zero, the result will be the following:

After exploration with WriteUp I, I have seen that the value of a alters the amplitude of the graph; the value of b alters the periodicity of the graph; and the value of c shifts the graph either to the left or to the right. It is valuable for students to also examine operations on the functions in order to view how these operations again, alter the graphs, thus changing the amplitude, periodicity and location of origin.

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