4 a) Shown above is a graph of the function _ 5122+2 mgc f($)_{4a:2, m>c Using the slider, or otherwise, determine the value of the constant e such that the function f is continuous. at = a: b) Now consider the function (a3) x2+2, 33395 g _ 4x1,3:>d Using Desmos, or otherwise, determine the two values of d, that make 9 continuous. Give your answers in ascending order. 5% : a: or a: c) Why does 9 have two values of d that make it continuous, but 1' has only one? Select the correct answer from the following options. O Because 9(a) is always positive. 0 Because :32 + 2 = 4m 7 2 has exactly two real roots, but :32 + 2 = 4m 7 1 has only one real root. O Because 9(d) : d2 + 14. 0 Because :32 + 2 = 4m 7 2 has exactly one real root, but 2:2 + 2 = 4.1: i 1 has two real roots. O Because 9(3) is defined as a piecewise function. 0 Because y = 4m 7 2 has a negative yintercept, but the y-intercept of y = 4a: 7 1 is positive. 0 None of these