Question 1179654
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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.<br>
Here is an example similar to yours with different parameters.<br>
{{{f(x) = -2sin(3(x+pi/4))+1}}}<br>
(1) Parent function: {{{sin(x)}}}
{{{graph(800,400,-pi,3pi,-6,6,sin(x))}}}<br>
(2) Innermost parentheses: {{{sin(x+pi/4)}}}
The graph is shifted pi/4 units left (green vs. red)
{{{graph(800,400,-pi,3pi,-6,6,sin(x),sin(x+pi/4))}}}<br>
(3) Other parentheses: {{{sin(3(x+pi/4))}}}
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)
{{{graph(800,400,-pi,3pi,-6,6,sin(x),sin(x+pi/4),sin(3(x+pi/4)))}}}<br>
(4) Multiplication: {{{-2(sin(3(x+pi/4)))}}}
The graph is stretched vertically by a factor of 2 and reflected across the x-axis (purple vs. blue)
{{{graph(800,400,-pi,3pi,-6,6,sin(x),sin(x+pi/4),sin(3(x+pi/4)),-2(sin(3(x+pi/4))))}}}<br>
(5) Addition: {{{-2(sin(3(x+pi/4)))+1}}}
The graph is shifted up 1 unit (yellow vs. purple)
{{{graph(800,400,-pi,3pi,-6,6,sin(x),sin(x+pi/4),sin(3(x+pi/4)),-2(sin(3(x+pi/4))),-2(sin(3(x+pi/4)))+1)}}}<br>