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Function Notation 1 Function Notation Intro y = 2x – 2 or y = 5x – 3 For function notation, we use “f(x)” in place of “y” For functions, the two notations mean the exact same thing, but "f(x)" gives you more flexibility and more information. The expression "f(x)" means "plug a value for x into a formula f 2 Why do we need this…? In textbooks and when writing things out, we use names like f(x), g(x), h(x), s(t), etc. With this notation, you can now use more than one function at a time without confusing yourself or mixing up the formulas. 3 Function Notation You used to say "y = 2x + 3; solve for y when x = –1". Now you say "f(x) = 2x + 3; find f(–1).” You do exactly the same thing in either case: you plug in –1 for x and then solve. f(-1) = 2(-1) + 3 = -2 + 3 =1 4 So… y = 2x +1 means the same thing as f(x) = 2x + 1 5 Solving the linear equation f(x) = g(x) Given: f(x) = 2x – 3 g(x) = 5x + 7 Find the solution for f(x) = g(x). To solve this problem, all we have to do is set the two functions equal to each other and then solve for x. 6 2x – 3 = 5x + 7 2x – 3 = 5x + 7 7 What is the solution for x in the equation f(x) = g(x), where F(x) = -5x + 4 + x and g(x) = 4x – 16 8 What is the solution for x in the equation f(x) = g(x), where F(x) = 4(x – 2) and g(x) = 4(2x – 3) 9 What is the solution for x in the equation f(x) = g(x), where f(x) = 24x – 48 and g(x) = 5x – 10 10 What is the solution for x in the equation f(x) = g(x), where f(x) = 5 + 25x and g(x) = -20x + 95 11 What is the solution for x in the equation f(x) = g(x), where f(x) = 32 – 3x and g(x) = 6x – 49 12 What is the solution for x in the equation f(x) = g(x), where f(x) = 5 and g(x) = 5x 13 What is the solution for x in the equation f(x) = g(x), where f(x) = 18x + 24 – 16x + 8 and g(x) = -2x + 16 14 What is the solution for x in the equation f(x) = g(x), where F(x) = 2.5x – 4.8 and g(x) = -1.5x + 91.2 15 What is the solution for x in the equation f(x) = g(x), where F(x) = 2x + 6 and g(x) = 4x – 12 3 3 16 What is the solution for x in the equation f(x) = g(x), where F(x) = x + 2 and g(x) = x – 3 4 5 17 18 19 20