SOLUTION: Find the equation of a sine wave that is obtained by shifting the graph of y=sin(x) to the right 9 units and downward 8 units and is vertically stretched by a factor of 4 when comp

Question 689126: Find the equation of a sine wave that is obtained by shifting the graph of y=sin(x) to the right 9 units and downward 8 units and is vertically stretched by a factor of 4 when compared to y=sin(x).
Found 2 solutions by stanbon, exodus:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the equation of a sine wave that is obtained by shifting the graph of y=sin(x) to the right 9 units and downward 8 units and is vertically stretched by a factor of 4 when compared to y=sin(x).
-------
Ans: y = 4sin(x-9)-8
===========================
cheers,
Stan H.
Answer by exodus(1) (Show Source): You can put this solution on YOUR website!
The general equation that should be formed is as follows:
y - A = Bsin(x - C)
where:
A stands for a vertical shift (if A is positive, move is upward; if A is negative, move is downward)
B stands for vertical stretch factor
C stands for a horizontal shift (if C is positive, move is to the right; if C is negative, move is to the left).
We start with the sine wave in 'home' position, having equation y = sin(x) which is really as follows:
y - 0 = 1sin(x - 0)
with
A = 0, (no vertical shift or change)
B = 1, (normal stretch factor or 'amplitude')
C = 0, (no horizontal shift or change)
so, the equation required is as follows:
y - (-8) = 4sin(x - 9)
which can simplify to
y + 8 = 4sin(x - 9)
or, if final equation is given in the form "y in terms of x" (also called 'making y the subject'), then:
y = 4sin(x - 9) - 8

RELATED QUESTIONS
Write an equation of the graph that results from shifting the graph of the following... (answered by macston)
Starting with the graph of f(x)=6^x , write the equation of the graph that results from (answered by Edwin McCravy)
Here is a big question and I'm not even sure where to begin, any help would be greatly... (answered by solver91311)
Well here it goes, write an equation for the parabola that is obtained by shifting the (answered by stanbon)
The graph of y = 0.2 ∣x - 3 ∣ + 3.9 can be obtained by shifting horizontally... (answered by MathLover1)
A sine wave test generator is an electronics labaratory can deliver two sine signals to a (answered by fractalier)
Describe a function g(x) in terms of f(x) if the graph of g is obtained by vertically... (answered by MathLover1)
Explain how the graph of g is obtained from the graph of f. a. f(x) = x^3, g(x)=(x-4)^3 (answered by stanbon)
Did I do this correctly? A function f is given, and the indicated transformations are... (answered by ewatrrr)