Day 4 examples
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This document discusses graphing composite functions. It provides examples of composing two functions f(x) and g(x), such as finding (f ◦ g)(x) and (g ◦ f)(x), and graphing the resulting composite functions. The document emphasizes determining the domains of the composite functions by considering the restrictions on the domains of the original functions. It also gives examples of finding equations for composite functions f(g(x)) and g(f(x)) and stating their domains and ranges.
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Day 4 examples
- 1. Graphing Composite Functions Warm-up Consider f(x) = √x - 1 and g(x) = x2 Determine (f ◦ g)(x) and (g ◦ f)(x) To find the domain of (f ◦ g)(x) you must consider the restrictions on the domain of g(x) and the new restrictions for (f ◦ g)(x)
- 2. Ex 2) Let f(x) = x + 1 and g(x) = x2. Find the equation of each composite function, graph it, and state its domain and range. a) y = f(g(x)) b) y = g(f(x)) c) y = f(f(x)) d) y = g(g(x))
- 4. Ex. Determine possible functions f and g so that: a) f(g(x)) = (x - 2)2 b) f(g(x)) = √x + 3
- 5. Assignment: p.314 #3, 4, 5, 6, 10