Question

Need help explaining these transformations that take place in this function
Y=3sinx to 3sin1/2(x-pi/2)

Answer 1

Is the new function \(y=3\sin(\frac{1}{2}(x-\pi/2))\)?

Answer 2

If it is, then you just have a shift right and horizontal stretch.

Answer 3

yep its a new functions im pretty sure and how muc of a shift to the right and horizontal shift?

Answer 4

Well lets think about it. If I have a function \(y=f(x)\), then what can I do to \(f(x)\) to make it such that all x's have to be, say, 3 larger than they actually are to have the same value (shift right by 3)?

Answer 5

yea

Answer 6

What do you mean 'yea'? I asked you a question.

Answer 7

oh and also the question ask for what the amp is and period and alsophase shift and what is the 1/4 wave?

Answer 8

and yes it has to be by 3

Answer 9

Calm down! we're not done with the first one. I AM ASKING YOU, if you have the function \(y=f(x)\), how do you shift right by 3?

Answer 10

f(-3)

Answer 11

no that gives the value of y AT -3. But you're close. Generalize for all x's.

Answer 12

x= -3

Answer 13

so all x's move over 3 units right

Answer 14

yes x-3 not = -3

Answer 15

so now we have f(x-3), which is a right shift by 3. What if I wanted to stretch all x values by a factor of 5? I need all values to be 5 times as big, just to equal the original f(x-3).

Answer 16

x^5 or x*5

Answer 17

Which one do you think. If I want 5x to be the same as x, then what do I multiply the 5 x by?

Answer 18

if you want the 5x to be the same as x? x1?

Answer 19

yes. you get it by multiplying by 1/5. if I transform f(x) with f(x 1/5) then I will have a horizontal stretch by a factor of 5, since x values need to be five times as large to equal what they were in f(x).

Answer 20

ok ic that

Answer 21

good. Then if I want a horiz shift of 3 and horiz stretch of 5 to f(x), what does it become?

Answer 22

3/5?

Answer 23

or is it 5/3?

Answer 24

NO! did i just get nothing done?
f(x) - shift horizontally -> f(x-3)
f(x-3) - stretch horizontally -> f((x-3) (1/5))

Answer 25

now, if I let f(x) = 3sin x, then I shifted horizontally by a and stretched horizontally by 1/b, then what does it look like now?