Question

Three functions are shown.

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 need to analyze their equations or slopes.

1. **Function A**: This function is a linear function that passes through the points (0, 2) and (6, 7).
To find the slope (rate of change), we use the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.833
\]

2. **Function B**: Function B does not have an explicit equation accessible, but we can estimate the slope by looking at the provided values:
- From (0, 2.50) to (6, 7.09):
\[
\text{slope} = \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765
\]
This is lower than the slope of Function A.

3. **Function C**: This function is given as \(y = 1.3x + 1\). The slope of this linear function is clearly \(1.3\).

Now, we can compare the rates of change:
- Function A: \( \approx 0.833 \)
- Function B: \( \approx 0.765 \)
- Function C: \( 1.3 \)

Ordering these from least to greatest rate of change, we have:

1. Function B (approx. 0.765)
2. Function A (approx. 0.833)
3. Function C (1.3)

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