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Function A

Function B
\begin{tabular}{|c|c|c|c|c|}
\hline [tex]$x$[/tex] & 0 & 2 & 4 & 6 \\
\hline [tex]$y$[/tex] & 2.50 & 4.03 & 5.56 & 7.09 \\
\hline
\end{tabular}

Function C
[tex]$
y=1.3 x+1
$[/tex]

Drag the functions to order them from LEAST to GREATEST rate of change.

Least [tex]$\qquad$[/tex] Greatest
[tex]$\square$[/tex] [tex]$\square$[/tex] [tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
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]
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