Three functions are shown.

Question

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