#1**+1 **

First one

4sin (x - 3) [remember that a "-" shifts the function to the right ]

Second one

Look at this

4(1/2) sin (x) + 2 + 6 = 2sin (x) + 8

So....it is vertically stretched by a factor of 4 and shifted up 6 units

Third one

The number out front doesn't affect the shift up/down...it just changes the amplitude of the curve....the midline of the graph remains the same

The number added or subtracted to the function affects the shift up/down

So.....shifting this sine graph [and its midline ] up 4 units results in f(x) = 4 + sin (x)

Look at the graph here : https://www.desmos.com/calculator/gnp4zjdwvs

CPhill Mar 8, 2019

#2**+1 **

Question 1 makes sense

However, for question 2, where did the 4 and 6 come from in the equation?

For question 3, just to make sure my response was correct then ? Im bit confused if thats what you were saying

jjennylove
Mar 8, 2019

#3**+2 **

Second one

Multiplying (1/2) by a factor of 4 produces a vertical stretch of 2

Adding 6 to 2 shifts the graph up 6 units and produces the "8"

So (1/2)sin (x) + 2 is transformed to 4(1/2)sin (x) + 2 + 6 = 2sin (x) + 8

Third one

Your answer of 4 sin (x) just increases the amplitude ( the "peaks" and "valleys" ) of the curve....it does not do anything to the shift

To shift the curve up by 4 units we need f(x) = 4 + sin (x) (the second answer )

CPhill Mar 8, 2019