SOLUTION: 4. Graph f(x) = 3sin(2x) + 2 over the interval [0, 2π] on the set of axes below. (4 points)

SOLUTION: 4. Graph f(x) = 3sin(2x) + 2 over the interval [0, 2π] on the set of axes below. (4 points) | |

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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Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Graph over the interval [, ]:

make table:
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|...if ,
|...if ,
|...if ,
|...if ,

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

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.

Here is the graph of 3sin(2x)+2:

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