Question

Based on the tables, describe the difference from Linear Function 1 to Linear Function 2.

Linear Function 1

x f(x)
1 2
1 3
2 3

Linear Function 2

x f(x)
1 7
6 3
2 8

The outputs from Linear Function 2 are increased by ??? units.

Answer 1

To compare Linear Function 1 and Linear Function 2, we need to analyze the provided data for each function and determine the difference in the outputs (f(x)) for corresponding x values where applicable.

**Linear Function 1:**
- For x = 1, f(x) = 2 and f(x) = 3 (values at the same x repeat).
- For x = 2, f(x) = 3.

**Linear Function 2:**
- For x = 1, f(x) = 7.
- For x = 6, f(x) = 3 (not applicable for the comparison as x = 6 does not appear in Linear Function 1).
- For x = 2, f(x) = 8.

Now, let's find the f(x) outputs for common x-values.

1. At **x = 1**:
- Linear Function 1: f(1) = 2 (and also 3, but we take one for comparison)
- Linear Function 2: f(1) = 7
- The difference is \( 7 - 2 = 5 \) (or \( 7 - 3 = 4 \), depending on which value you consider).

2. At **x = 2**:
- Linear Function 1: f(2) = 3
- Linear Function 2: f(2) = 8
- The difference is \( 8 - 3 = 5 \).

From the above comparisons:
- At x = 1, the difference in the output values of Linear Function 2 compared to Linear Function 1 is either 4 or 5, depending on the value from Linear Function 1 you consider.
- At x = 2, the difference is 5.

Since the statement asks for a consistent increase, we can conclude that the outputs from Linear Function 2 are generally increased by **5 units** when compared to the corresponding outputs of Linear Function 1 where applicable.