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Lesson 1.5 Read: Pages 62-68 Page 58: #1-29 (EOO), 37-61 (EOO) Combinations of Functions Objective Students will know how to find arithmetic combinations and compositions of functions. Use the graph of f and g to graph h(x)=(f + g)(x). Find (a) (f + g)(x) (b) (f - g)(x) (c) (fg)(x) and (d) (f/g)(x). What is the domain of f/g? Use a graphing utility to graph the functions f, g, and h in the same viewing window. Find (a) f g , (b) g f, and, if possible, (c) ( f g )(0) 𝑓 𝑥 = 3𝑥 + 5 𝑔 𝑥 = 𝑥3 + 1 Determine the domains of (a) 𝑓, (b) 𝑔, and (c) f g . Use a graphing utility to verify your results. 𝑓 𝑥 = 𝑥+3 𝑥 𝑔 𝑥 = 2 3 𝑓 𝑥 = 2 𝑥 −1 𝑔 𝑥 =𝑥+1 Find (a) 𝑓(𝑔 𝑥 ), 𝑔(𝑓 𝑥 ), and the domain of 𝑓 𝑔 𝑥 . Determine algebraically whether 𝑓 𝑔 𝑥 = 𝑔(𝑓 𝑥 ). (b) Use a graphing utility to graph 𝑓(𝑔 𝑥 ) and 𝑔(𝑓 𝑥 ) and complete a table of values to confirm 𝑓 𝑔 𝑥 = 𝑔(𝑓 𝑥 ). 𝑓 𝑥 = 1 𝑥4 𝑔 𝑥 = 𝑥4 𝑓 𝑥 = 𝑥3 − 4 𝑔 𝑥 = 3 𝑥 + 10 Use the graphs of f and g to evaluate the functions. (𝑓 − 𝑔)(1) (𝑓𝑔)(4) ( f g )(1)