Let’s analyze the graph provided to determine the amplitude and period of the function.

Step 1: Amplitude

The amplitude of a sinusoidal function is the maximum distance from the midline of the graph to its highest or lowest point.

From the graph:

• The maximum value is approximately 1.5.
• The minimum value is approximately -1.5.
• The midline (average of max and min) is at 0.

Thus, the amplitude is: $\text{Amplitude} = \frac{\text{Max} - \text{Min}}{2} = \frac{1.5 - (-1.5)}{2} = \frac{3}{2} = 1.5$

Step 2: Period

The period is the length of one complete cycle of the graph.

From the graph:

• One complete cycle starts at x = 0, peaks at x ≈ 0.5, returns to the midline at x ≈ 1, hits the trough at x ≈ 1.5, and completes at x = 2.
• The distance between these points shows the period is: $\text{Period} = 2$

Final Answer:

• Amplitude: $1.5$
• Period: $2$

Would you like further details or a deeper breakdown of the calculations?

Related Questions:

1. What is the formula of a sinusoidal function given its amplitude and period?
2. How can you determine the phase shift of a sinusoidal function from its graph?
3. How does changing the amplitude affect the graph of a sinusoidal function?
4. How does the period relate to the frequency of a sinusoidal function?
5. What are the maximum and minimum points of this graph in terms of coordinates?

Tip:

To find the period of a sinusoidal function quickly, look at the distance between consecutive peaks (or troughs).