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

Least ----------------------------------------> Greatest
(blank) (blank) (blank)
Options for the blanks: Function A, Function B, Function C

Answer 1

To determine the rate of change for each of the functions, we can analyze each one.

1. **Function A:** The line passing through the points (0, 2) and (6, 7) has a slope (rate of change) given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.83
\]

2. **Function B:** To find the rate of change for Function B, we can calculate the average rate of change between the given points:
- Between (0, 2.50) and (2, 4.03):
\[
\text{slope} = \frac{4.03 - 2.50}{2 - 0} = \frac{1.53}{2} \approx 0.765
\]
- Between (2, 4.03) and (4, 5.56):
\[
\text{slope} = \frac{5.56 - 4.03}{4 - 2} = \frac{1.53}{2} \approx 0.765
\]
- Between (4, 5.56) and (6, 7.09):
\[
\text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} \approx 0.765
\]
- The average rate of change for Function B appears to be approximately 0.765.

3. **Function C:** The function is expressed as \( y = 1.3x + 1 \), so the rate of change (slope) is clearly 1.3.

Now we can order the functions based on their rates of change:
- Function A: \( \approx 0.83 \)
- Function B: \( \approx 0.765 \)
- Function C: \( 1.3 \)

Ordering from LEAST to GREATEST rate of change, we have:
1. Function B (≈ 0.765)
2. Function A (≈ 0.83)
3. Function C (1.3)

So, the correct order is:

Least ----------------------------------------> Greatest
Function B Function A Function C