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Notes Over 2.2 Identifying Functions - Numerically Decide whether the relation is a function. 1. Input Output 2. 1, 4, 1, 2, 3, 4, 5, 4 2 1 A function, because every 4 3 input goes to only one output 5 8 7 Not a function, because 4 goes to both 3 and 5 Notes Over 2.2 Identifying Functions - Verbally Decide whether the relation is a function. 3. In a school basketball game, all ticket prices are the same. The input value x is the number of tickets purchased, and the output y is the total price paid. A function, because every input goes to only one output 4. The input value x is the number of times you cast your line in fishing, and the output y is the total number of fish caught. Not a function, because you could throw your line in 5 times one day and catch 2 fish and another day throw it in 5 times and not catch anything. Notes Over 2.2 Identifying Functions - Graphically Decide whether the relation is a function. 5. Vertical line test 1 1 2 3 2 2 A function, because it only hits the graph once all the way across. Notes Over 2.2 Identifying Functions - Graphically Decide whether the relation is a function. 6. Vertical line test Not a function, because it hits the graph more than once from -5 to 5. Notes Over 2.2 Identifying Functions - Algebraically Decide whether the relation is a function. 7. x y 17 Try to solve for y y x 17 A function, because every input goes to only one output 8. y x 17 y x 17 y x 17 y x 17 Not a function, because most inputs will have 2 outputs Notes Over 2.2 Identifying Functions 9. f x 9x 2 Find f(-2), f(5), and f(x - 3) f 2 9 2 2 18 2 16 f 5 95 2 45 2 47 f x 3 9x 3 2 9x 27 2 9 x 25 Notes Over 2.2 Evaluating a Piecewise Function Evaluate the function for the given value of x. x 1, if x 1 f x x 2, if x 1 10. f 1 x2 1 2 3 11. f 3 x 1 3 1 4 Notes Over 2.2 Finding the Domain of a Function Find the domain of each function. 1 f x 2 x 9 f x x 3 x5 12. f x x7 Domain excludes x-values that result in division by 0. Domain excludes x-values that result in even roots of negative numbers. All real numbers x7 Notes Over 2.2 Finding the Domain of a Function Find the domain of each function. 13. f x x 16 2 x 16 0 x 4x 4 0 Closed Circles l -6 l l -4 l l -2 l l 0 4 4 2 These are critical values l l 2 l , 4 4, l 4 l l 6 Notes Over 2.2 Function Application 14. Andre Agassi hit a lob in tennis right on his baseline that took a path given by the function: f x 0.015625x 1.25x 3 2 where x and y are measured in feet. If a tennis court is 78 feet long, will the ball land in, assuming he hit it straight? f x 0.01562578 1.2578 3 f x 5.4375 2 No, because it is still coming down. Notes Over 2.2