Three functions are shown.

Question

The graph titled function A has a line passing through the points (0, 2) and (6, 7).

Function B
x 0 2 4 6
y 2.50 4.03 5.56 7.09

Function C
y = 1.3x + 1

Drag the functions to order them from least to greatest rate of change.

Answer 1

To determine the rate of change for each function, we can analyze each one:

1. Function A: This is a linear function, and we can find the slope (rate of change) by calculating the change in \(y\) over the change in \(x\) between the two given points (0, 2) and (6, 7).

   \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.83 \]

2. Function B: This function is a set of specific points. To estimate the rate of change between the points:

   • From \( (0, 2.50) \) to \( (2, 4.03) \): \[ \text{slope} = \frac{4.03 - 2.50}{2 - 0} = \frac{1.53}{2} \approx 0.765 \]
   • From \( (2, 4.03) \) to \( (4, 5.56) \): \[ \text{slope} = \frac{5.56 - 4.03}{4 - 2} = \frac{1.53}{2} \approx 0.765 \]
   • From \( (4, 5.56) \) to \( (6, 7.09) \): \[ \text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} \approx 0.765 \] The average rate of change is approximately 0.765.

3. Function C: This is a linear function defined by the equation \(y = 1.3x + 1\). The slope (rate of change) is the coefficient of \(x\), which is 1.3.

Now we can compare the rates of change:

• Function A: \(\frac{5}{6} \approx 0.83\)
• Function B: Approximately \(0.765\)
• Function C: \(1.3\)

Ordering them from least to greatest rate of change:

1. Function B: \(0.765\)
2. Function A: \(0.83\)
3. Function C: \(1.3\)

Thus, the order from least to greatest rate of change is: Function B, Function A, Function C.

Answer 2

you sure?

Answer 3

Let’s double-check the rates of change for each function to ensure accuracy.

1. Function A: A line through the points (0, 2) and (6, 7): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.8333 \]

2. Function B: Given points (0, 2.50), (2, 4.03), (4, 5.56), (6, 7.09). We can calculate the rate of change:

   • From \( (0, 2.50) \) to \( (2, 4.03) \): \[ \text{slope} = \frac{4.03 - 2.50}{2 - 0} = \frac{1.53}{2} = 0.765 \]
   • From \( (2, 4.03) \) to \( (4, 5.56) \): \[ \text{slope} = \frac{5.56 - 4.03}{4 - 2} = \frac{1.53}{2} = 0.765 \]
   • From \( (4, 5.56) \) to \( (6, 7.09) \): \[ \text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} = 0.765 \] The average rate of change across all segments is about \(0.765\).

3. Function C: The equation \(y = 1.3x + 1\) has a slope of: \[ \text{slope} = 1.3 \]

Now, for clarity, let’s summarize the rates of change:

• Function A: \( \approx 0.8333 \)
• Function B: \( 0.765 \)
• Function C: \( 1.3 \)

Ordering them from least to greatest:

1. Function B: \(0.765\)
2. Function A: \(0.8333\)
3. Function C: \(1.3\)

So, the correct order from least to greatest rate of change is Function B, Function A, Function C.

Thank you for prompting me to verify; the original response regarding the order was indeed accurate.