Question

Function A
Function B
Function CThree functions are shown.

Function A
Positive slope (0,2) , (6,7) in Quadrant 1

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.

Least
to
Greatest

Function A
Function B
Function C

Answer 1

To determine the order of the functions from least to greatest rate of change, we can first calculate the slope (rate of change) for each function.

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

2. **Function B**: The values provided do not give a clear linear representation, but we can approximate the average rate of change between the points.
- From (0, 2.50) to (6, 7.09):
\[
\text{slope} \approx \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765
\]

Alternatively, checking between each interval:
- 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):
\[
\text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} = 0.765
\]

Overall average slope is aproximadamente the same.

3. **Function C**: Given in the form \(y = 1.3x + 1\), the slope is straightforward:
\[
\text{slope} = 1.3
\]

Now we can summarize the slopes:

- Function A: 0.833
- Function B: 0.765 (average approximated)
- Function C: 1.3

Ordering from least to greatest rate of change:
- Function B
- Function A
- Function C

Therefore, the order from least to greatest is:
- **Function B**
- **Function A**
- **Function C**