Question 1159754: 4. Graph f(x) = 3sin(2x) + 2 over the interval [0, 2π] on the set of axes below. (4 points)
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Graph the function by looking at how the parent function sin(x) is modified.
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.
Here is the graph of the parent function sin(x):
First transformation: parentheses
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.
Here is the graph of sin(2x):
Second transformation: multiplication
3sin(2x) compared to sin(2x) stretches the graph vertically by a factor of 3.
Here is the graph of 3sin(2x):
Third transformation: addition
3sin(2x)+2 compared to 3sin(2x) translates the graph vertically by 2 units.
