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.
Image not found

Least ----------------------------------------> Greatest

Function A Function B Function C

Answer 1

To determine the rate of change for each function, we should calculate the slope or rate of change for each function.

1. **Function A**:
The slope can be calculated using the two points (0, 2) and (6, 7).
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.833
\]

2. **Function B**:
We can approximate the slope using the provided points. We can take the change between the first and last points.
\[
\text{slope} = \frac{y_6 - y_0}{x_6 - x_0} = \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765
\]

3. **Function C**:
The equation is given in slope-intercept form \(y = mx + b\) where \(m\) is the slope. For Function C:
- The rate of change (slope) is \(1.3\).

Now we have calculated the slopes:
- Function A: \( \approx 0.833 \)
- Function B: \( \approx 0.765 \)
- Function C: \( 1.3 \)

Ordering them from least to greatest:
1. Function B (approximately 0.765)
2. Function A (approximately 0.833)
3. Function C (1.3)

So the order from LEAST to GREATEST rate of change is:
- Function B
- Function A
- Function C

Therefore, you should drag them in this order:
**Function B, Function A, Function C**