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.
Image not found

Least ----------------------------------------> Greatest

Function A Function B Function C

Answer 1

To determine the rate of change for each function, we should calculate the slope or rate of change for each function.

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

2. Function B: We can approximate the slope using the provided points. We can take the change between the first and last points. \[ \text{slope} = \frac{y_6 - y_0}{x_6 - x_0} = \frac{7.09 - 2.50}{6 - 0} = \frac{4.59}{6} \approx 0.765 \]

3. Function C: The equation is given in slope-intercept form \(y = mx + b\) where \(m\) is the slope. For Function C:

   • The rate of change (slope) is \(1.3\).

Now we have calculated the slopes:

• Function A: \( \approx 0.833 \)
• Function B: \( \approx 0.765 \)
• Function C: \( 1.3 \)

Ordering them from least to greatest:

1. Function B (approximately 0.765)
2. Function A (approximately 0.833)
3. Function C (1.3)

So the order from LEAST to GREATEST rate of change is:

• Function B
• Function A
• Function C

Therefore, you should drag them in this order: Function B, Function A, Function C