The table represents a function.

x y
0 −5
2 1
3 4
5 10
Complete the statement by selecting from the drop-down menu.

The rate of change in the function ​y=x−6​ is
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the rate of change of the function represented in the table.

1 answer

To find the rate of change of the function \( y = x - 6 \), we can analyze it. This is a linear function with a constant rate of change (slope). The slope of \( y = x - 6 \) is \( 1 \) because the coefficient of \( x \) is \( 1 \).

Now, let's calculate the average rate of change using the values from the table. The rate of change between any two points \((x_1, y_1)\) and \((x_2, y_2)\) can be computed as:

\[ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's calculate the rate of change using two pairs of points from the provided table:

  1. From \( (0, -5) \) to \( (2, 1) \): \[ \text{Rate} = \frac{1 - (-5)}{2 - 0} = \frac{1 + 5}{2} = \frac{6}{2} = 3 \]

  2. From \( (2, 1) \) to \( (3, 4) \): \[ \text{Rate} = \frac{4 - 1}{3 - 2} = \frac{3}{1} = 3 \]

  3. From \( (3, 4) \) to \( (5, 10) \): \[ \text{Rate} = \frac{10 - 4}{5 - 3} = \frac{6}{2} = 3 \]

In all cases, the average rate of change of the function represented in the table is \( 3 \).

Now, we complete the statement:

The rate of change in the function \( y = x - 6 \) is \( 1 \), which is less than the rate of change of the function represented in the table, which is \( 3 \).

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