Final answer:
The graph of g(x) = |f(x)| is related to the graph of f(x) by reflecting the portion of the graph of f(x) that is below the x-axis to be above the x-axis.
Step-by-step explanation:
The graph of the function g(x) = |f(x)| is related to the graph of f(x) by reflecting the portion of the graph of f(x) that is below the x-axis to be above the x-axis. In other words, if there are any points (x, y) on the graph of f(x) where y is negative, the corresponding point on the graph of g(x) will have the same x-coordinate but a positive y-coordinate.
For example, consider the function f(x) = -2x, where 0 ≤ x ≤ 20. The graph of f(x) is a straight line that starts at (0, 0) and goes downwards with a slope of -2. The graph of g(x) = |f(x)| is the same as the graph of f(x) from x = 0 to x = 20, except that the portion of the graph below the x-axis is reflected to be above the x-axis.
You can see this relationship between the graphs by considering specific values of x. For example, when x = 5, f(5) = -10, so g(5) = |-10| = 10. The point (5, 10) is on the graph of g(x) but not on the graph of f(x).