Question

Provide an example of a trig function and describe how it is transformed from the standard trig function f(x) = sin x, f(x) = cos x, or f(x) = tan x using key features.

Thanks!

Answer 1

Let us consider the trigonometric function, g(x) = 2sin(x - 4) + 3

Now this function g(x) can be obtained from f(x) = sin(x) by applying several transformations.

The transformations are given below.

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At first, if we shift the graph of f(x) horizontally to the right by 4 units, then the graph becomes the graph of f(x) = sin(x - 4)

Then if we stretch the new graph vertically by 2 units, then the graph becomes the graph of f(x) = 2sin(x - 4)

Next if we shift the graph vertically upwards by 3 units, then the graph becomes the graph of g(x) = 2sin(x - 4) + 3