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Rutgers University-Camden 640:121 Calculus I Assignment 1.3 1. Consider the graph of y = f(r) drawn below: Sketch graphs of each of the following functions: (a) y = f(x) +2 (b) y = f(x - 3) (c) y = ;f(I) (d) y = -f(I) 2. Use transformations on an appropriate standard function to sketch a graph of y = 2vr + 1. 3. Use transformations on an appropriate standard function to sketch a graph of y = 1 + sin(xx). 4. Find all solutions for e that satisfy each of the following equations: (a) 4 cose sin # + 3 cose = 0 (b) 2 tane + (sec #)? = 4 5. Let G(x) = VI+1 Write functions f(r) and g(x) such that G = fog, where neither f nor g is the identity function. 6. Let H(t) = tant 1 + tant Write functions f(t) and g(t) such that H = fog, where neither f nor g is the identity function. (See next page.)7. Consider the following table of values: I 1 2 3 4 5 6 f (1) 3 1 4 2 2 5 g(x) 6 3 2 1 2 3 Determine the value of each of the following expressions: (a) f(g(1)) (b) g(f (1)) (c) f(f(1)) (d) g(g(1)) (e) (go f)(3) (f) (fog)(6)