Question

Write the equation of the periodic function based on the graph.

(1 point)
Responses

y=−4cosx
y equals negative 4 cosine x

y=−14cosx
y equals negative Start Fraction 1 over 4 End Fraction cosine x

y=−4sinx
y equals negative 4 sine x

y=4cosx

Answer 1

To determine the correct equation of the periodic function from the options provided, we need to examine certain properties of the periodic function, including amplitude, period, phase shift, and whether it uses sine or cosine.

1. **Amplitude**: The amplitude is the height of the wave from its midline to its peak, so if the peak value is 4 and the lowest value is -4, the amplitude is 4.

2. **Direction**: If the graph is flipped vertically (peaks pointing down), the equation will involve a negative sign. This indicates that the graph starts from the trough rather than the peak.

3. **Cosine vs. Sine**: A cosine function typically starts at its maximum or minimum value. In contrast, the sine function starts from the midline (0). If the graph starts at a minimum, it's likely a negative cosine function.

Based on this analysis:

- **y = -4cos(x)** suggests that the graph starts at the minimum (downward peak) at its maximum height of -4, which fits the features of a function that is shifted downward.

Therefore, the equation of the periodic function is likely:

**y = -4cos(x)**