1. **Problem Statement:** Determine the following characteristics from the wave pool graph of Sara's height above the pool bottom: a) Period b) Number of Cycles c) Maximum Height d) Minimum Height e) Equation of the Axis f) Amplitude g) Domain h) Range 2. **Understanding the Problem:** The graph shows a periodic wave oscillating between approximately 0.4 meters and 2.0 meters over the time interval from 1 to 8 seconds. 3. **Step-by-step Solution:** 1. **Period:** The period is the length of one complete cycle of the wave. From the graph, one cycle starts at about 1 second and repeats at about 4 seconds. So, $$\text{Period} = 4 - 1 = 3 \text{ seconds}$$ 2. **Number of Cycles:** The total time interval is from 1 to 8 seconds, which is 7 seconds. Number of cycles $$= \frac{7}{3} \approx 2.33$$ cycles. 3. **Maximum Height:** The highest point on the graph is approximately $$2.0$$ meters. 4. **Minimum Height:** The lowest point on the graph is approximately $$0.4$$ meters. 5. **Equation of the Axis:** The axis is the horizontal line halfway between the max and min heights. $$\text{Axis} = \frac{2.0 + 0.4}{2} = \frac{2.4}{2} = 1.2$$ meters. 6. **Amplitude:** Amplitude is the distance from the axis to the maximum (or minimum) height. $$\text{Amplitude} = 2.0 - 1.2 = 0.8$$ meters. 7. **Domain:** The domain is the time interval shown on the graph. $$\text{Domain} = [1, 8] \text{ seconds}$$ 8. **Range:** The range is the vertical interval of the wave. $$\text{Range} = [0.4, 2.0] \text{ meters}$$ --- **Final answers:** a) Period: 3 seconds b) Number of Cycles: approximately 2.33 c) Maximum Height: 2.0 meters d) Minimum Height: 0.4 meters e) Equation of the Axis: $y = 1.2$ f) Amplitude: 0.8 meters g) Domain: $[1, 8]$ h) Range: $[0.4, 2.0]$