Answer:
#1. The graph has a maximum at 5.
#2. The graph has an amplitude of 5.
Explanation:
Maximum
The maximum of a cosine graph is the greatest y-value attained at the peak of the curve.
From observation of the given graph, the maximum y-value is y = 5. Therefore, the graph has a maximum at 5.
Amplitude
The amplitude of a cosine graph is the vertical distance between the mid-line and the peak (or trough). In other words, it is half the positive difference between the maximum and minimum y-values.
The maximum of the given graph is y = 5 and the minimum is y = -5. Therefore, the difference is 10 units. This means the amplitude is half of that difference. So, the graph has an amplitude of 5.
x-intercept
The x-intercepts of a graph are the points at which the graph intersects or crosses the x-axis, representing the values of x for which the corresponding y-values are zero.
Given the cosine graph does not intersect or cross the x-axis when x = 5, the graph does not have an x-intercept at (5, 0).
Conclusion
The following statements about the graphed cosine function are correct:
- #1. The graph has a maximum at 5.
- #2. The graph has an amplitude of 5.