Question

what is the rate of change of the function represented by the table?

\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline 1 & 5 \\\\ \\hline 2 & 5 \\\\ \\hline 3 & 5 \\\\ \\hline 4 & 5 \\\\ \\hline \\end{array}$$

• 0
• 1
• 4
• 5

Explanation:

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<reasoning>

Identify coordinates from the table

We select two points from the table to calculate the rate of change. Let's choose:
\[(x_1, y_1) = (1, 5)\]
\[(x_2, y_2) = (2, 5)\]

Apply the rate of change formula

The rate of change is the ratio of the change in \(y\) to the change in \(x\):
\[\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}\]

Calculate the values

Substitute the coordinates into the formula:
\[\text{Rate of Change} = \frac{5 - 5}{2 - 1} = \frac{0}{1} = 0\]
</reasoning>

<answer>
<mcq-correct>(A) 0</mcq-correct>
<mcq-option>(B) 1</mcq-option>
<mcq-option>(C) 4</mcq-option>
<mcq-option>(D) 5</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify coordinates from the table

We select two points from the table to calculate the rate of change. Let's choose:
\[(x_1, y_1) = (1, 5)\]
\[(x_2, y_2) = (2, 5)\]

Apply the rate of change formula

The rate of change is the ratio of the change in \(y\) to the change in \(x\):
\[\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}\]

Calculate the values

Substitute the coordinates into the formula:
\[\text{Rate of Change} = \frac{5 - 5}{2 - 1} = \frac{0}{1} = 0\]
</reasoning>

<answer>
<mcq-correct>(A) 0</mcq-correct>
<mcq-option>(B) 1</mcq-option>
<mcq-option>(C) 4</mcq-option>
<mcq-option>(D) 5</mcq-option>
</answer>

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