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.

1 answer

To compare Linear Function 1 and Linear Function 2, we need to analyze the sets of values provided for each function.

Linear Function 1:

  • For \( x = 1 \), \( f(x) \) takes the values 2 and 3 (it appears that there are two different outputs for the same input).
  • For \( x = 2 \), \( f(x) = 3 \).

This function does not strictly represent a linear relationship, as linear functions typically have a single output for each input. The outputs for \( x = 1 \) indicate that this function is not a simple linear function.

Linear Function 2:

  • For \( x = 1 \), \( f(x) = 7 \).
  • For \( x = 6 \), \( f(x) = 3 \).
  • For \( x = 2 \), \( f(x) = 8 \).

Like Linear Function 1, Linear Function 2 also does not exhibit constant output for a given input, but it has distinct outputs at different inputs.

Comparative Analysis:

  • The output values in Linear Function 2 appear consistently higher than those in Linear Function 1. Specifically, comparing corresponding values where possible:
    • For \( x = 1 \): Linear Function 1 outputs a maximum of 3, while Linear Function 2 outputs 7 (an increase).
    • For \( x = 2 \): Linear Function 1 outputs 3, while Linear Function 2 outputs 8 (again an increase).
    • For \( x = 6 \), Linear Function 2 has a unique input and output not corresponding to Linear Function 1.

From this analysis, we can conclude that:

  • Linear Function 2's outputs are higher than those from Linear Function 1 overall.
  • The adjustments of output suggest a vertical shift of the function values, as indicates that the outputs from Linear Function 2 consist of an overall increase in values compared to Linear Function 1.

In summary, Linear Function 2 can be viewed as a modified version of Linear Function 1, shifted upward by an inconsistent amount but predominantly demonstrating higher output values across the identified inputs.