Question 1159754
<br>
{{{y = 3sin(2x)+2}}}<br>
Graph the function by looking at how the parent function sin(x) is modified.<br>
The order of the transformations is the order in which you would evaluate the function for a given value of x.  The "3" is a multiplication; the "(2x)" is in parentheses; the "+2" is addition.  According to standard rules of order of operations, the order is (1) parentheses, (2) multiplication, and (3) addition.<br>
Here is the graph of the parent function sin(x):<br>
{{{graph(400,200,0,2pi,-6,6,sin(x))}}}<br>
First transformation: parentheses<br>
sin(2x) compared to sin(x) means the graph completes two periods instead of one on [0,2pi] -- i.e., the period of the function is cut in half, from 2pi to pi.  Note this is often viewed as a horizontal compression by a factor of 2.<br>
Here is the graph of sin(2x):<br>
{{{graph(400,200,0,2pi,-6,6,sin(2x))}}}<br>
Second transformation: multiplication<br>
3sin(2x) compared to sin(2x) stretches the graph vertically by a factor of 3.<br>
Here is the graph of 3sin(2x):<br>
{{{graph(400,200,0,2pi,-6,6,3sin(2x))}}}<br>
Third transformation: addition<br>
3sin(2x)+2 compared to 3sin(2x) translates the graph vertically by 2 units.<br>
Here is the graph of 3sin(2x)+2:<br>
{{{graph(400,200,0,2pi,-6,6,3sin(2x)+2)}}}<br>