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Translations and Combinations Algebra 5/Trigonometry Shifting What does it mean to shift? (interactive) Vertical Shift c Units Up: h(x) = f(x) + c Vertical Shift c Units Down: h(x) = f(x) – c Vertical Shift c Units Right: h(x) = f(x - c) Vertical Shift c Units Left: h(x) = f(x + c) Try These f ( x) x g ( x) x 2 m( x ) x 2 h( x) | x | j ( x) | x 1 | n( x) | x | 1 Reflecting What does it mean to reflect? (interactive) Reflection in the x-axis: h(x) = -f(x) Reflection in the y-axis: h(x) = f(-x) Try These f ( x) x g ( x) x h( x) | x | j ( x) | x | Stretching Try These f ( x) x g ( x) 3 x m( x ) 1 x 2 h( x ) | x | 1 |x| 2 n( x ) 2 | x | j ( x) Arithmetic Combinations of Functions Sum: (f + g)(x) = f(x) + g(x) Difference: (f - g)(x) = f(x) - g(x) Product: (fg)(x) = f(x) ∙ g(x) f ( x) f Quotient: ( )(x) = g ( x) , g ( x) 0 g Compute f(x) = 4x + 2 and g(x) = 2x – 1 f(x) + g(x) f(x) - g(x) fg(x) ( f )(x) g Now Try These f(x) = x2 - 9 and g(x) = 3x – 1 f(x) + g(x) f(x) - g(x) fg(x) ( f )(x) g Composition of Two Functions The composition of the function f with the function g is given by (f o g)(x) = f(g(x)) The domain of (f o g) is the set of all x in the domain of g such that g(x) is in the domain of f. Compositions Given: f(x) = x2 - 9 and g(x) = 3m, find f(g(x)). find g(f(x)). Now Try These Given f(x) = 6x + 2 and g(x) = 2x – 1 find f(g(x)). find g(f(x)).