Question

Three functions are shown.

Function A

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 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 compare the rate of change of the three functions, we need to analyze each function carefully.

**Function A**: This function has points at (0, 2) and (6, 7). To find the rate of change (slope), we can use the formula:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.8333
\]

**Function B**: Given the values in a table (0, 2.50), (2, 4.03), (4, 5.56), (6, 7.09), we can calculate the average rate of change over the interval from x = 0 to x = 6:

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

To check the rate of change over smaller intervals:
- From (0, 2.5) 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):
\[
\text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} = 0.765
\]

Thus, the average rate of change for Function B also comes out to be approximately 0.765.

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

Now that we have determined the rate of change for each function:

- **Function A:** Slope ≈ 0.8333
- **Function B:** Average slope ≈ 0.765
- **Function C:** Slope = 1.3

Ordering from least to greatest rate of change:

1. Function B (approximately 0.765)
2. Function A (approximately 0.8333)
3. Function C (1.3)

So, the correct order is:

- **Least:** Function B
- Function A
- **Greatest:** Function C