Final answer:
To write a piecewise function from given points (2,3) and (6,0), we use different definitions for different intervals. For x ≤ 2, f(x) = 3. For 2 < x ≤ 6, f(x) = -x + 5. For x > 6, f(x) = 0.
Step-by-step explanation:
To write a piecewise function for the given points (2,3) and (6,0), we need to define the function differently for different intervals. Let's denote the function as f(x). For x ≤ 2, f(x) = 3 because the y-coordinate is 3 when x = 2. For 2 < x ≤ 6, f(x) = -x + 5 because the line passing through the two points has a slope of -1 and a y-intercept of (0, 5). For x > 6, f(x) = 0 because the y-coordinate is 0 when x = 6.