To find the rate of change for each function and then order them from least to greatest, we need to analyze the data provided for Functions B and C. Let's go through each function step-by-step.
### Function A
- Function A doesn't provide any equation or data points, so we cannot determine its rate of change.
### Function B
We are given the following table of values for Function B:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 2 & 4 & 6 \\
\hline
y & 2.50 & 4.03 & 5.56 & 7.09 \\
\hline
\end{array}
\][/tex]
#### Step-by-Step Calculation for Rate of Change:
1. Calculate the rate of change between each consecutive pair of points:
[tex]\[
\text{rate between } (0, 2.50) \text{ and } (2, 4.03) = \frac{4.03 - 2.50}{2 - 0} = \frac{1.53}{2} = 0.765
\][/tex]
[tex]\[
\text{rate between } (2, 4.03) \text{ and } (4, 5.56) = \frac{5.56 - 4.03}{2} = \frac{1.53}{2} = 0.765
\][/tex]
[tex]\[
\text{rate between } (4, 5.56) \text{ and } (6, 7.09) = \frac{7.09 - 5.56}{2} = \frac{1.53}{2} = 0.765
\][/tex]
2. Average rate of change for Function B:
Since each rate of change is consistently 0.765, the average rate of change for Function B is also [tex]\(0.765\)[/tex].
### Function C
Function C is given by the equation [tex]\( y = 1.3x + 1 \)[/tex].
#### Step-by-Step Calculation for Rate of Change:
1. The rate of change in a linear equation of the form [tex]\( y = mx + b \)[/tex] is the slope, [tex]\( m \)[/tex].
2. Here, the slope [tex]\( m \)[/tex] is [tex]\( 1.3 \)[/tex].
### Comparison and Ordering
We have calculated the rates of change:
- Rate of change for Function B: [tex]\( 0.765 \)[/tex]
- Rate of change for Function C: [tex]\( 1.3 \)[/tex]
Since Function A's rate of change is undetermined, we will not include it in our ordering.
### Final Ordering from LEAST to GREATEST:
[tex]\[
0.765 \quad 1.3
\][/tex]
So, based on the rates of change:
- Least: Function B (rate of change = [tex]\( 0.765 \)[/tex])
- Greatest: Function C (rate of change = [tex]\( 1.3 \)[/tex])
The correct order is:
Least [tex]$\quad$[/tex] Greatest [tex]$\quad$[/tex] [tex]$\boxed{\text{Function B}} \quad \boxed{\text{Function C}}$[/tex]
