SOLUTION: https://gyazo.com/ca2b8a4784e42cfbe233efc64cf657d2

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Question 1179654: https://gyazo.com/ca2b8a4784e42cfbe233efc64cf657d2
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


For the order of transformations, use the order in which you would evaluate the function for a given value of x, using standard rules of order of operations: parentheses first; multiplication next; addition last.

Here is an example similar to yours with different parameters.

f%28x%29+=+-2sin%283%28x%2Bpi%2F4%29%29%2B1

(1) Parent function: sin%28x%29
graph%28800%2C400%2C-pi%2C3pi%2C-6%2C6%2Csin%28x%29%29

(2) Innermost parentheses: sin%28x%2Bpi%2F4%29
The graph is shifted pi/4 units left (green vs. red)
graph%28800%2C400%2C-pi%2C3pi%2C-6%2C6%2Csin%28x%29%2Csin%28x%2Bpi%2F4%29%29

(3) Other parentheses: sin%283%28x%2Bpi%2F4%29%29
The period is shortened by a factor of 3 (divided by 3); there are now 3 full periods where there was a single period of the parent function (blue vs. green)


(4) Multiplication: -2%28sin%283%28x%2Bpi%2F4%29%29%29
The graph is stretched vertically by a factor of 2 and reflected across the x-axis (purple vs. blue)


(5) Addition: -2%28sin%283%28x%2Bpi%2F4%29%29%29%2B1
The graph is shifted up 1 unit (yellow vs. purple)