Name ______________________________________________ Date __________________________________ Thurgood Marshall Academy Public Charter High School – Pre-Calculus Notes #11 – Function Notation for Ordered Pairs Topic: General Properties of Functions Objectives: 11.1 Given a two-variable equation, answer questions about its solutions posed in function notation. Standards: A. A-REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Is each of the following relations a function? Yes or no. {(5,2), (−3, 8), (3, −8), (5, 4)} {(3,2), (4,2), (5, 2), (−3, 2)} B. We often use letters as names for relations. These letters are not _________________________. Suppose f is the relation whose ordered pairs are the solutions of 𝑦 = 2𝑥 − 3. Name three ordered pairs belonging to f. mrmerlintma.wordpress.com C. “(5, w) is an ordered pair in the relation named g. Find w.” If g is not a function, then there might be __________________ correct answers to this question. “(5, w) is an ordered pair in the relation named g. Find w.” If g is a function, then there is no more than _______________ correct answer to this question: D. 𝑓(5) = 7 means that the ordered pair ___________ belongs to the function named f. We can only use this notation if f is a ______________________________. If f is a relation but not a ____________________________, then 𝑓(5) would not necessarily equal one specific number. E. Suppose the function named g contains the ordered pairs that satisfy 𝑦 = 2𝑥 − 3. True or false: 𝑔(4) = 5? What is 𝑔(−3)? Find 𝑚 such that 𝑔(𝑚) = −11. mrmerlintma.wordpress.com Practice Exercises #11 – Function Notation for Ordered Pairs 11.1 Given a two-variable equation, answer questions about its solutions posed in function notation. 1. Suppose g contains the ordered pairs satisfying 𝑥 − 𝑦 = 10. Find 𝑔(−4). 2. f is the function containing all of the ordered pairs satisfying 𝑦 = −2𝑥 − 3. Find m so that 𝑓(𝑚) = −11. 3. Suppose the function named g contains the ordered pairs that satisfy 𝑦 = √𝑥 + 2 − 3. True or false: 𝑔(2) = −1? What is 𝑔(14)? Find 𝑎 such that 𝑔(𝑎) = 0. mrmerlintma.wordpress.com 4. Suppose k contains the ordered pairs satisfying 𝑦 = 3𝑥 + 1. Find 𝑘(5). 5. Suppose m contains the ordered pairs satisfying 𝑦 = −𝑥 + 1. Find w such that 𝑚(𝑤) − 3. 6. Suppose p contains the ordered pairs satisfying 𝑥 − 𝑦 = 12. Find 𝑝(4). 7. Suppose p contains the ordered pairs satisfying 𝑥 − 𝑦 = 12. Find x such that 𝑝(𝑥) = −9. mrmerlintma.wordpress.com 8. Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 3 . Find 𝑓(−3). 9. Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 2 + 1. Find 𝑓(−3). 10. Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 4 + 𝑥. Find 𝑓(−2). 11. Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 2 − 5𝑥 − 9. Find 𝑓(−3). mrmerlintma.wordpress.com 12. Suppose 𝑔 contains the ordered pairs satisfying 𝑥 = √𝑦 + 3. Find x such that 𝑔(𝑥) = 22. 13. Suppose f contains the ordered pairs satisfying 𝑦 = −(𝑥 + 3)2 . Find 𝑓(−1). 14. Suppose g contains the ordered pairs satisfying 𝑦 = |𝑥 2 + 2𝑥 + 1|. Find 𝑓(−5). 15. Suppose f contains the ordered pairs satisfying 𝑦 = 4 𝑥 + 2. Find 𝑓(12). 3 mrmerlintma.wordpress.com 3 16. Suppose f contains the ordered pairs satisfying 𝑥 = − 5 𝑦 − 11. Find m such that 𝑓(𝑚) = 20. 17. Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 + 2. Find m such that 𝑓(𝑚) = 20. 18. Suppose f contains the ordered pairs satisfying 𝑥 = − 5 𝑦 − 11. Find 𝑓(10). 3 4 3 mrmerlintma.wordpress.com 19. Suppose f contains the ordered pairs satisfying 𝑦 = 2𝑥+1 . 3 20. Suppose h contains the ordered pairs satisfying 𝑥 = 3𝑦−1 . 2 3 Find 𝑓 (2). 2 Find n such that 𝑓(𝑛) = 3. ANSWERS 1. -14 2. 4 3. True, 1, 7 4. 16 5. 4 6. -8 7. 3 8. -27 9. 10 10. 14 11. 15 12. 5 13. -4 14. 16 15. 11 16. -33 17. 24 18. -35 19. 4/3 20. 1/2 mrmerlintma.wordpress.com