To determine the correct graph of the function \( y = 4\sin(x) \), we need to create a table of values for this function. The key characteristics of \( y = 4\sin(x) \) are:
- The amplitude is 4, meaning the maximum value is 4 and the minimum value is -4.
- The period of the sine function is \( 2\pi \).
- The function oscillates between -4 and 4 as \( x \) varies.
Here is a table of values for \( y = 4\sin(x) \) at selected values of \( x \):
| \( x \) | \( y = 4\sin(x) \) | |---------------|------------------------| | \( 0 \) | \( 4\sin(0) = 0 \) | | \( \frac{\pi}{2} \) | \( 4\sin\left(\frac{\pi}{2}\right) = 4 \) | | \( \pi \) | \( 4\sin(\pi) = 0 \) | | \( \frac{3\pi}{2} \) | \( 4\sin\left(\frac{3\pi}{2}\right) = -4 \) | | \( 2\pi \) | \( 4\sin(2\pi) = 0 \) |
Table Summary of Values
| \( x \) | \( y \) | |-----------------|------------------| | \( 0 \) | \( 0 \) | | \( \frac{\pi}{2} \) | \( 4 \) | | \( \pi \) | \( 0 \) | | \( \frac{3\pi}{2} \) | \( -4 \) | | \( 2\pi \) | \( 0 \) |
Characteristics to Look For:
- The graph should reach a maximum of 4 at \( x = \frac{\pi}{2} \) and a minimum of -4 at \( x = \frac{3\pi}{2} \).
- The graph should cross the x-axis at \( x = 0, \pi, 2\pi \).
Now that we have these key points and characteristics, you can compare them with the graphs provided (Graph A, Graph B, Graph C) to identify which graph corresponds to \( y = 4\sin(x) \).
If you see a graph that reaches a maximum of 4 and a minimum of -4, while maintaining the sine wave shape, that would be the correct graph for \( y = 4\sin(x) \).
If you provide descriptions of the graphs, I could further assist in identifying the correct one!