# How do I write the equations of these tranformed graphs? Help?1.)Write the equation of the transformed graph of tangent with period 4 that has been shifted vertically up 3 units.  2.) Write the equation of the transformed graph of sine with period that has been shifted vertically up 3 units and has an amplitude of . (3 points) 14. Write the equation of the transformed graph of sine with period that has been shifted horizontally to the right 3 units, has an amplitude of , and has been flipped across the x-axis.

## Expert Answers

We can only answer one question per post, so I will answer the third question and give general directions:

The general function looks like `y=Asin(B(x-h))+k` (or any of the other trigonometric functions in place of sine.) The base function is sinx. The following transformations will occur:

A: A is the amplitude (a vertical stretch (|A|A>1) or compression(|A|<1).) If A<0 then the function is reflected across the x-axis.

B: B affects the period; B is obtained by `B=(2pi)/p` where p is the period. In effect, B is a horizontal stretch (|B|<1) or compression (|B|>1). If B<0 then the base function is reflected across the y-axis.

h: h is a horizontal translation or shift.

k: k is a vertical translation or shift. In the case of sin or cos, it is the midline.

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We are given the sine function with period `pi` , a horizontal shift right of 3 units, an amplitude of 3/4 and reflected over the x-axis.

A: Since the amplitude is 3/4 and the function is reflected across the x-axis, we have A=-3/4.

B: Since the period is `pi` , we have `B=(2pi)/pi==>B=2`

h: The function is translated 3 units right so h=3.

k: There is no vertical translation given, so k=0.

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The function is `y=-3/4sin(2(x-3))`

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The graph of sinx and the transformed graph:

Approved by eNotes Editorial Team

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