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5.3 Figure 1 below is a sketch of the graphs of functions f (red curve) and g (blue curve). .Y g (-1,0) (0,0) (2,0) -3 x (1.-1) -2 (0-2) -31 -4 (1.-4) Figure 1. a. C. If f(x) = ax + bx+c for some specific a,b,c eR, use Figure 1 to answer the following questions. Determine the value of c. (1) b. Without computing a , explain why a >0. (2) Determine all values of x for which f is increasing. (1) d. Determine the equation for g as a piecewise function. (3) e. Give the biggest subset of D, such that g is decreasing and g'exists. Further, give the equation for g' on this subset. (2) f. Determine algebraically whether f is odd, even, or neither. (2) 8

QUESTION 5 [22 Marks] . 5.1 Letſ be a function such that f is an odd function, $(x) = 0 only for x = *** where kez, k Ik 2 D, ER, and R, ={y|-25 y 2 a. Determine the set of all the x-intercepts of f. b. Is f symmetric? Explain. Give a possible equation for f. . (1) (1) (3) ୭ 5.2 Let f(x) = tan x and g(x) = In (x + 2). Determine the following a. Domain and range for f , and for g. b.fig and its domain. c. Range for fog. d. g 'together with its domain and range. DSER (2) (1) (1) (2)