Given any sinusoidal equation, how do you identify the type of transformations that are made?

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Given any sinusoidal equation, how do you identify the type of transformations that are made?

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Answer 1 · 2018-03-12T15:43:58

Example: Describe the transformations to get $g (x) = 2 sin (3 (x + \frac{π}{4})) + 2$ $g(x) = 2sin(3(x + pi/4)) + 2$ from $f (x) = sin x$ $f(x) = sinx$

Here are what each of the parameters in the equation $y = a sin (b (x - c)) + d$ $y = asin(b(x -c)) + d$ :

$a \to$ $a ->$ vertical stretch
$\frac{1}{b} \to$ $1/b ->$ horizontal stretch
$c \to$ $c ->$ phase shift
$d \to$ $d ->$ vertical transformation

So in the given equation, we have a vertical stretch by a factor of $2$ $2$ , a horizontal stretch by a factor of $\frac{1}{3}$ $1/3$ , a transformation $\frac{π}{4}$ $pi/4$ units left and a transformation $2$ $2$ units up.

Hopefully this helps!

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Given any sinusoidal equation, how do you identify the type of transformations that are made?

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