Functions and Function Notation Notes PDF

Functions and Function Notation Notes What is a Function: § A function is a set of ordered pairs in which each x-value has only ONE y-value associated with it. § For every x there can only be one y. § Has to pass th...

Functions and Function Notation Notes What is a Function: § A function is a set of ordered pairs in which each x-value has only ONE y-value associated with it. § For every x there can only be one y. § Has to pass the vertical line test. Tell if the following are functions. X Y X Y { (2,3), (3,5), (6,5), (6, 3), (8,10) } -1 1 -15 12 0 2 -10 20 3 7 -5 30 { (-1,7), (-6,8), (1,4),(4,11) (5, 11) } 3 9 0 30 6 12 5 35 10 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 1 3 2 5 3 7 4 9  Functions and Function Notation Notes Function Notation: New name for functions! Old: y=…. New: f(x)=… Everything works the same way as with “y=” notation! Function notation f(x): Pronounced: “f of x” Means: the value of function at x Indicates: x is the variable in the function We can use letters other than f such as g or h. Example: Given an x-value, find the value of f(x) f(3) means evaluate f(x) when x=3 If f(x) = 3x-15, then f(3) = 3(3)-15 So, f(3) = -6 Find f(7) when f(x) = (1/7)x²+5 Algebraic Calculator Find h(3) when h(x) = 12x²-3x+1 Algebraic Calculator  Functions and Function Notation Notes Find f(4) when f(x) = ½ (8x-4) Algebraic Calculator Given g(x) = -8x-2 If g(x) = -26, find x Algebraic Calculator Given h(x) = 3(2x-4)+2 If h(x) = 20, find x Algebraic Calculator  Functions and Function Notation Notes The graph represents a function f(x). The graph represents a function f(x). 1. What is f(-8)? 4. What is f(-6)? 2. What is f(6)? 5. What is f(0)? 3. What is x when f(x) = 2? 6. What is x when f(x) = -8? Translate the following statements into coordinate points: 1. 𝑓 5 = −1 2. 𝑔 −2 = 0 3. ℎ 6 = 6