Describe the changes in the graph of the following funciton

t(h) = -2/3sin(h) + 1

To describe the changes in the graph of the function t(h) = -2/3sin(h) + 1, we need to understand the effect of each component of the function on the graph.

1. Amplitude: The amplitude of a sine function determines the maximum distance that the graph will deviate from its center line. In this case, the coefficient in front of the sine function is -2/3. The absolute value of this coefficient is 2/3, which represents the amplitude. Therefore, the graph of t(h) will oscillate between 1 + 2/3 = 5/3 and 1 - 2/3 = 1/3.

2. Vertical Shift: The term "+1" in the function represents a vertical shift. It shifts the entire graph vertically upwards by 1 unit. Therefore, the center line of the graph will be raised to y = 1.

3. Phase Shift: There is no specific term in the function that indicates a phase shift. So, the graph of t(h) = -2/3sin(h) + 1 will start at its equilibrium position (center line) when h = 0.

4. Period: The period of a sine function is the distance between two consecutive peaks or troughs. In this case, there is no multiplier for the variable "h", which means the period remains unchanged and is equal to 2π.

Combining all these factors, we can describe the changes in the graph of t(h) = -2/3sin(h) + 1 as follows:
- The graph oscillates between 5/3 and 1/3.
- The center line is shifted upwards to y = 1.
- The graph starts at its equilibrium position when h = 0.
- The period of the function is 2π.

Please note that to visualize the exact shape and details of the graph, it is recommended to graph the function using appropriate software or a graphing calculator.