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 order the functions A, B, and C from least to greatest rate of change, we need to determine the rate of change for each function.

1. **Function A**:
- The line passes through the points (0, 2) and (6, 7).
- The rate of change (slope) can be calculated using 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**:
- The given values are:
- At \( x = 0 \), \( y = 2.50 \)
- At \( x = 2 \), \( y = 4.03 \)
- At \( x = 4 \), \( y = 5.56 \)
- At \( x = 6 \), \( y = 7.09 \)
- We can calculate the average rate of change between points to determine the slope:
- 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 will serve as a rough gauge of the average rate for function B.

3. **Function C**:
- The function is given as \( y = 1.3x + 1 \).
- The slope (rate of change) is the coefficient of \( x \), which is **1.3**.

Now we can compare the rates of change:

- Function A: \( \approx 0.833 \)
- Function B: \( \approx 0.765 \)
- Function C: \( 1.3 \)

Ordering these values from least to greatest rate of change:

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

Thus, the ordered functions from least to greatest rate of change are:
**B, A, C**.