Final answer:
The graph of a function with domain [0,∞) must be entirely contained in quadrants I and IV of a two-dimensional coordinate plane because these are the regions where x is positive, in accordance with the function's domain.
Step-by-step explanation:
If Miranda knows that the domain of f(x) is the set of positive real numbers, which means [0,∞), and she graphs f(x) on a coordinate plane, then the graph must be entirely contained in quadrants I and IV. These are the quadrants where x takes on positive values. Quadrant I contains points where both x and y are positive, making it compatible with functions that have positive outputs. Quadrant IV, on the other hand, contains points where x is positive, but y is negative, suitable for functions with negative outputs. Since the domain is all positive real numbers, the x-values will never be negative, so the graph won't extend into quadrants II or III.
A straightforward example to consider is the graph of a constant function f(x) = 20 for 0 ≤ x ≤ 20. Here, the graph is a horizontal line at y = 20, stretching from the y-axis (x=0) to x=20. It is entirely contained within quadrant I because all x-values are positive and the y-value (f(x)) is also positive.
In cases of quadrants and graphing, it's important to know that the two-dimensional (x-y) graphing system is based on four quadrants, with the positive x-axis pointing right (towards quadrant I and IV) and the positive y-axis pointing up (towards quadrants I and II).