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# Check my 3 Algebra questions

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3 If you can check the above question and for this one I am unsure.  Mar 8, 2019
edited by jjennylove  Mar 8, 2019

#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   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 )   Mar 8, 2019