Review the graph of f(x) = RootIndex 5 StartRoot x EndRoot and the graph of the transformed function g(x). On a coordinate plane, y = f (x) curves up through (negative 1, negative 1) to inflection point (0, 0), and then curves up through (1, 1). Y = g (x) curves down through (negative 5, 2) to inflection point (negative 4, 0), and then curves down through (negative 3, negative 2) and (4, negative 3). If g(x) = a · f(x + b), how is f(x) transformed to get g(x)? –2f(x + 4) –2f(x – 4) –f(x + 4) –f(x – 4)

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.