Question

Create a table of values to determine which is the correct graph of y=4sinx . (1 point) Responses It is not possible to determine which graph is the graph of y=4sinx . It is not possible to determine which graph is the graph of y equals 4 sine x . Graph B Graph B Graph A Graph A Graph C

Answer 1

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:

1. The graph should reach a maximum of 4 at \( x = \frac{\pi}{2} \) and a minimum of -4 at \( x = \frac{3\pi}{2} \).
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!