Question

Three functions are shown

Function A: A graph with the point (0, 2)

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 order of the functions from least to greatest rate of change, we will analyze each function:

1. **Function A**: The only information given is the point (0, 2). Without more information about the behavior of this function (e.g., whether it is linear, quadratic, etc.), we cannot determine its rate of change.

2. **Function B**: You have a set of x and y values. To find the rate of change, we can calculate the average rate of change between the points provided:

- Between (0, 2.50) and (2, 4.03):
\[
\text{Rate} = \frac{4.03 - 2.50}{2 - 0} = \frac{1.53}{2} = 0.765
\]
- Between (2, 4.03) and (4, 5.56):
\[
\text{Rate} = \frac{5.56 - 4.03}{4 - 2} = \frac{1.53}{2} = 0.765
\]
- Between (4, 5.56) and (6, 7.09):
\[
\text{Rate} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} = 0.765
\]

It appears that nearly all segments yield a similar average rate of change of about 0.765.

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

Comparing the rates of change:

- **Function A**: Unable to determine rate of change.
- **Function B**: Average rate of change approximately 0.765.
- **Function C**: Rate of change of 1.3.

Without complete information for Function A, we cannot place it in the proper order. However, based on the rates of change known:

1. **Function B**: 0.765 (average rate of change)
2. **Function C**: 1.3 (rate of change)

Thus, **the order from least to greatest rate of change (assuming Function A has a rate of change less than 0.765)** would be:

1. Function A (if its rate of change is less than 0.765)
2. Function B
3. Function C

If Function A has a higher rate of change, it would go at the end. Please provide more information about Function A for a complete ordering.