Final answer:
The question focuses on matching transformations of the function f(x) = 2x - 6 with their descriptions, which involves identifying shifts, stretches/compressions, and reflections based on changes to the function's equation.
Step-by-step explanation:
The question is referring to identifying transformations of the function f(x) = 2x - 6. Transformations in this context could include shifting the graph of the function up or down (vertical shift), left or right (horizontal shift), stretching or compressing it vertically (vertical stretch/compression), or flipping it over the x-axis (reflection).
To match each transformation with its description, we need to look for changes in the function's equation. For example:
- A function of the form f(x) = 2x - 6 + k where k is a positive number represents a vertical shift upwards by k units.
- A function of the form f(x) = 2(x - h) - 6 where h is positive represents a horizontal shift to the right by h units.
- A function of the form f(x) = a(2x - 6) where a is greater than 1 represents a vertical stretch by a factor of a.
- If a is negative, the function reflects over the x-axis, in addition to being stretched or compressed.
Understanding these transformations allows you to graph the function with various alterations, matching them to their respective descriptions.