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

Answer 1

To determine the rate of change of each function, we can look at the slope for the linear functions and analyze the data for function B.

1. Function A: The points (0, 2) and (6, 7) provide us the slope. $$\text{slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{7-2}{6-0}=\frac{5}{6}\approx 0.833$$

2. Function B: We can calculate the change in $y$ over the change in $x$ between the values given:

   • From $(0,2.50)$ 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 $(6,7.09)$: $$\text{slope}=\frac{7.09-5.56}{6-4}=\frac{1.53}{2}=0.765$$ The slope for function B is approximately constant at about $0.765$.

3. Function C: The equation $y=1.3x+1$ has a slope of $1.3$.

Now, comparing the rates of change:

• Function B: $\approx 0.765$
• Function A: $\approx 0.833$
• Function C: $1.3$

Ordering from least to greatest rate of change:

• Function B (0.765)
• Function A (0.833)
• Function C (1.3)

So the order is: Function B, Function A, Function C.