Question

Write the equation of the transformed graphs of each trigonometric function

Answer 1

The equations of the transformed graphs are $y = \tan(\frac{\pi}{4}x) + 3$ and $y = -\frac34\sin(2x)$

How to transform the functions?

The tangent function

The parent function is:

y = Atan(Bx) + k

It has a period of 4.

So, we have:

$\frac{\pi}{B} = 4$

Make B the subject

$B = \frac{\pi}{4}$

It is shifted vertically up by 3 units.

So, we have:

k = 3

Substitute these values in y = Atan(Bx) + k and remove A

$y = \tan(\frac{\pi}{4}x) + 3$

Hence, the equation of the transformed graph is $y = \tan(\frac{\pi}{4}x) + 3$

The sine function

The parent function is:

y = Asin(Bx) + k

It has a period of $\pi$

So, we have:

$\frac{2\pi}{B} = \pi$

Make B the subject

B = 2

It has an amplitude of 3/4

So, we have:

A = 3/4

It is flipped across the x-axis

So, we have:

A = -3/4

Substitute these values in y = Asin(Bx) + k and remove k

$y = -\frac34\sin(2x)$

Hence, the equation of the transformed graph is $y = -\frac34\sin(2x)$

Read more about function transformation at:

brainly.com/question/13810353

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