Final answer:
To obtain a horizontal line from the parent function f(x) = x, a vertical compression and a shift upwards or downwards are required. The final graph of the function is restricted to the x-values from 0 to 20. Transformations are crucial for understanding how to visually represent functions.
Step-by-step explanation:
To determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g, it is essential to understand different types of transformations. The parent function f(x) = x is a linear function with a slope of 1, which means the graph is a straight line that passes through the origin and has an angle of 45 degrees with respect to the x-axis.
If we have a graph that is a horizontal line, as described, the transformation from the parent function is quite different. A horizontal line can be achieved by transforming the parent function f(x) = x into f(x) = c, where c is a constant value.
Therefore, the transformation sequence would likely include:
- Vertical compression to flatten the slope of the line
- A shift upwards or downwards depending on the value c
For the range 0 ≤ x ≤ 20, the graph of f(x) would be restricted between these x-values. The concept of transformations is fundamental in understanding how various functions are visually represented through their graphs.