Tomations of fon Based on the tables, describe the difference from Linear Function 1 to Linear Function 2. Linear Function 1 x f (x) 1 1 2 3 2 3 Linear Function 2 f(x); aligned 1 6\\ 2 7\\ 3 0 aligned (1 point)

Question

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

Answer 1

To compare Linear Function 1 and Linear Function 2, let's list their outputs based on the x-values provided in the tables:

Linear Function 1:

• When \( x = 1 \), \( f(1) = 1 \)
• When \( x = 2 \), \( f(2) = 3 \)
• When \( x = 3 \), \( f(3) = 3 \)

Linear Function 2:

• When \( x = 1 \), \( f(1) = 6 \)
• When \( x = 2 \), \( f(2) = 7 \)
• When \( x = 3 \), \( f(3) = 0 \)

Now let's calculate the differences in outputs for corresponding x-values:

1. For \( x = 1 \):

   • Linear Function 1: \( 1 \)
   • Linear Function 2: \( 6 \)
   • Difference: \( 6 - 1 = 5 \)

2. For \( x = 2 \):

   • Linear Function 1: \( 3 \)
   • Linear Function 2: \( 7 \)
   • Difference: \( 7 - 3 = 4 \)

3. For \( x = 3 \):

   • Linear Function 1: \( 3 \)
   • Linear Function 2: \( 0 \)
   • Difference: \( 0 - 3 = -3 \)

In summary:

• The outputs from Linear Function 2 are increased by 5 units when \( x = 1 \), by 4 units when \( x = 2 \), and decreased by 3 units when \( x = 3 \).

Thus, while the outputs are increased by a varying number of units, the specific increase for generalization isn't uniform. The overall trend shows an increase for the first two x-values and a decrease for the last.

Based on the consistently observed changes for \( x = 1 \) and \( x = 2 \):

The outputs from Linear Function 2 are increased by 5 and 4 units, respectively, for \( x = 1\) and \( x = 2\).

Therefore, we can summarize that the outputs from Linear Function 2 are increased by 5 units for \(x = 1\), by 4 units for \(x = 2\), and decreased by 3 units for \(x = 3\).