Question

All of the following represent the same function except _____.


{(0, 1), (2, 3), (4, 5), (7, 8)}
y = x - 1

x y
1 0
3 2
5 4
8 7

Answer 1

To determine which of the given representations does not represent the same function, we need to evaluate each one:

1. **Set of ordered pairs:** \(\{(0, 1), (2, 3), (4, 5), (7, 8)\}\)
- This set represents a function where the output for each input is defined. The pairs show that for each x-value, the corresponding y-value is given.

2. **Equation:** \(y = x - 1\)
- This is a linear equation. If we plug in the x-values (for example, 1, 3, 5, and 8), we will get the corresponding y-values:
- For \(x = 0\), \(y = 0 - 1 = -1\) (not in the list)
- For \(x = 2\), \(y = 2 - 1 = 1\) (matches)
- For \(x = 4\), \(y = 4 - 1 = 3\) (not in the list)
- For \(x = 7\), \(y = 7 - 1 = 6\) (not in the list)
- Thus, \(y = x - 1\) generates values that do not match all of those in the given pairs.

3. **Table of values:**
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 0 \\
3 & 2 \\
5 & 4 \\
8 & 7 \\
\hline
\end{array}
\]
- This table gives pairs of (x, y) values. If we look at the values:
- (1, 0)
- (3, 2)
- (5, 4)
- (8, 7)
- No input-output pair in this table matches the pairs from the first set.

Now, comparing the representations:

- The ordered pairs set does not match the linear equation \(y = x - 1\) for many x-values.
- The table of values also does not match the ordered pairs set.

However, the **equation** \(y = x - 1\) does not fully capture the outputs in the ordered pairs and also does not align with all the pairs in the table.

Thus, the correct answer is that the representation that does **not** represent the same function is the linear equation:

**y = x - 1**.