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.

Answer 1

To determine the rates of change of the three functions, we can analyze their slopes:

1. **Function A:**
The slope can be calculated using the two points (0, 2) and (6, 7).
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.8333
\]

2. **Function B:**
We can calculate the slope by determining the change in \( y \) divided by the change in \( x \) between the given points:
\[
\text{slope} \text{ (between (0, 2.50) and (6, 7.09))} = \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765
\]

3. **Function C:**
The slope is explicitly given in the equation \( y = 1.3x + 1 \), where the slope is \( 1.3 \).

Now, we can compare the calculated rates of change (slopes):

- Function B: \( \approx 0.765 \)
- Function A: \( \approx 0.8333 \)
- Function C: \( 1.3 \)

Ordering from least to greatest rate of change gives us:

- Function B (least)
- Function A
- Function C (greatest)

So the order from least to greatest rate of change is:

**Function B < Function A < Function C**