f(x)={0: x is less than or equal to -1, ax-b: -1 is less than x is less than 1, 3: x is greater than or equal to 1. (Piecewise function)

(2x +1, x54 x² +12, x>4 3. Is the function f(x) = continuous?

The function f(x) has a domain of [-9, 9] and is plotted below such that the portion of the graph on the interval (-2, 1) is hidden from view. Given that f(-2) = −3 and f(1) = 5, determine what conclusions can be drawn based on the Intermediate Value Theorem on the interval (-2, 1). -10-9-8-7 -6 -5 -4 -3 -2 Since the function f(x) is | Intermediate Value Theorem y ? ? ? ? ? ? r I r 1 I L I L I I 2 19 3 Graph of f 4 5 6 7 8 9 10 X ✓on its domain, the

Suppose that f(x) and g(x) are each one-to-one functions. Suppose also that f(2) = 5, f(5) = 6, g(6) = 5, g(5)= 3.5, and that g(2) = 6. Compute 1. f-¹ (g(6)) 2. f(g-¹ (6)) 3. g=¹(f(2)) = | 4. g(f ¹(5)) = =