Final answer:
To graph the piecewise function F(x) = {x^2+2 if -5 is less than or equal to x <3, x-4 if 3 is less than or equal to x <7, plot the two parts of the function separately on the same graph.
Step-by-step explanation:
To graph the piecewise function, we need to plot the two parts of the function separately on the same graph. First, for the interval -5 ≤ x < 3, we have f(x) = x^2 + 2. Begin by plotting points for this part of the function, such as (-5, 27), (-4, 18), (-3, 11), (-2, 6), (-1, 3), (0, 2), (1, 3), (2, 6), and (2.99, 11.95). Connect these points with a smooth curve. Next, for the interval 3 ≤ x < 7, we have f(x) = x - 4. Plot points for this part of the function, such as (3, -1), (4, 0), (5, 1), (6, 2), and (6.99, 3.99). Connect these points with a straight line. The final graph should have a curved portion and a straight line portion.