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

Answer 1

To determine the rate of change of each function, we can look at the slope for the linear functions and analyze the data for function B.

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

2. **Function B**: We can calculate the change in \( y \) over the change in \( x \) between the values given:
- 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 \( (6, 7.09) \):
\[
\text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} = 0.765
\]
The slope for function B is approximately constant at about \( 0.765 \).

3. **Function C**: The equation \( y = 1.3x + 1 \) has a slope of \( 1.3 \).

Now, comparing the rates of change:
- **Function B**: \( \approx 0.765 \)
- **Function A**: \( \approx 0.833 \)
- **Function C**: \( 1.3 \)

Ordering from least to greatest rate of change:
- Function B (0.765)
- Function A (0.833)
- Function C (1.3)

So the order is: **Function B, Function A, Function C**.