Questions: Question 3 1 pts The function represented by the table is neither quadratic nor linear because its average rate of change over consecutive intervals of equal length is neither constant nor linear x f(x) 100 10 200 9 300 7 400 4

Solution Steps

To determine whether the function is neither quadratic nor linear, we need to check the average rate of change over consecutive intervals of equal length. If the average rate of change is neither constant nor follows a linear pattern, the function is neither quadratic nor linear.

1. Calculate the average rate of change between each pair of consecutive points.
2. Check if these rates of change are constant or follow a linear pattern.
3. If neither condition is met, the function is neither quadratic nor linear.

To determine if the function is neither quadratic nor linear, we first calculate the average rate of change between each pair of consecutive points. The average rate of change between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the given data points: \[ (100, 10), (200, 9), (300, 7), (400, 4) \]

We calculate: \[ \text{Rate of Change between } (100, 10) \text{ and } (200, 9) = \frac{9 - 10}{200 - 100} = -0.01 \] \[ \text{Rate of Change between } (200, 9) \text{ and } (300, 7) = \frac{7 - 9}{300 - 200} = -0.02 \] \[ \text{Rate of Change between } (300, 7) \text{ and } (400, 4) = \frac{4 - 7}{400 - 300} = -0.03 \]

Next, we check if the rates of change are constant. A constant rate of change would mean that all calculated rates are equal: \[ -0.01 \neq -0.02 \neq -0.03 \] Since the rates of change are not equal, the function is not linear.

We then check if the rates of change follow a linear pattern. This would mean that the difference between consecutive rates of change is constant: \[ (-0.02 - (-0.01)) = -0.01 \] \[ (-0.03 - (-0.02)) = -0.01 \] The differences are constant, indicating a linear pattern in the rates of change.

Final Answer