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.
least -------------------------- greatest
function A function B function C

Answer 1

To determine the order of the functions from least to greatest rate of change, we need to calculate the rate of change for each function.

1. **Function A**: This function is a line that passes through the points (0, 2) and (6, 7). We can calculate the rate of change (slope) using the formula:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.83
\]

2. **Function B**: The values given are:
- (0, 2.50)
- (2, 4.03)
- (4, 5.56)
- (6, 7.09)

To find the rate of change, we can calculate the slope between the endpoints (0, 2.50) and (6, 7.09):

\[
\text{slope} = \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765
\]

3. **Function C**: This function is given in the linear form \( y = 1.3x + 1 \). The rate of change (slope) for this function is simply the coefficient of \( x \), which is 1.3.

Now we can summarize the rates of change:
- Function A: approximately 0.83
- Function B: approximately 0.765
- Function C: 1.3

Now, ordering these values from least to greatest:
1. Function B: 0.765
2. Function A: 0.83
3. Function C: 1.3

Thus, the final ordering from least to greatest rate of change is:
1. Function B
2. Function A
3. Function C

So, the answer is:
- Function B
- Function A
- Function C