A function is given. \[ h(t)=-t+\frac{6}{5} ; t=-6, t=1 \] (a) Determine the net change between the given values of the variable. (b) Determine the average rate of change between the given values of the variable. Need Help? Watch it

Let's solve the problem step by step. **Given Function:** \[ h(t) = -t + \frac{6}{5} \] **Given Values of \( t \):** \[ t = -6 \quad \text{and} \quad t = 1 \] --- ### **(a) Net Change Between the Given Values of the Variable** **Net Change** is calculated as the difference in the function's values at the two points: \[ \text{Net Change} = h(1) - h(-6) \] 1. **Calculate \( h(1) \):** \[ h(1) = -1 + \frac{6}{5} = -\frac{5}{5} + \frac{6}{5} = \frac{1}{5} \] 2. **Calculate \( h(-6) \):** \[ h(-6) = -(-6) + \frac{6}{5} = 6 + \frac{6}{5} = \frac{30}{5} + \frac{6}{5} = \frac{36}{5} \] 3. **Compute Net Change:** \[ \text{Net Change} = \frac{1}{5} - \frac{36}{5} = -\frac{35}{5} = -7 \] **Answer for (a):** \[ \boxed{-7} \] --- ### **(b) Average Rate of Change Between the Given Values of the Variable** **Average Rate of Change** is calculated using the formula: \[ \text{Average Rate of Change} = \frac{h(1) - h(-6)}{1 - (-6)} \] Using the values from part (a): \[ \text{Average Rate of Change} = \frac{-7}{1 + 6} = \frac{-7}{7} = -1 \] **Answer for (b):** \[ \boxed{-1} \] --- ### **Summary of Answers:** - **(a)** The net change is **-7**. - **(b)** The average rate of change is **-1**. If you need further clarification or assistance, feel free to ask!