2. 1.7 FUNCTIONS

3. CCSS Content Standards 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. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

4. You solved equation with elements from a replacement set. Determine whether a relation is a function. Evaluate functions.

5. What is a Function? A function is a rule that establishes a relationship with an input and an output. Input ( x )Output ( y ) DOMAIN RANGE

6. What is a Function? function – a relation where each input matches up with exactly one output Input ( x )Output ( y ) DOMAIN RANGE

7. x (inputs) y (outputs) 1 20 31 53 86 f relation – a pairing of input (domain) and output (range) numbers

8. x (inputs) y (outputs) 1 20 31 53 86 f relation – a pairing of input (domain) and output (range) numbers * A set of ordered pairs domain

9. x (inputs) y (outputs) 1 20 31 53 86 f relation – a pairing of input (domain) and output (range) numbers domain range Domain = D {1, 2, 3, 5, 8} Range = R {-1, 0, 1, 3, 6} independent dependent

10. xf (x) 3 03 13 33 63 63 33 Is f (x) a function? function – a relation where each input matches up with exactly one output If an input value is put in multiple times, you will get the same output every time. YES!

11. xf (x) 13 013 1-3 43 65 65 31 Is f (x) a function? WHY? Check yourself! Does each input match up with exactly one output? If an input value is put in multiple times, do you get the same output every time? NO!

12. How can I tell if it’s a function? REAL WORLD EXAMPLES

13. People vs. Places

14. Relation: Different Form {(1,-1),(2,0),(3,1),(5,6),(8,6)} Is this relation a function? Hint: Look at all of the input values first! {(1,-1),(2,0),(3,1),(5,6),(8,6)}

15. Relation: Different Form {(1,-1),(2,0),(3,1),(5,6),(2,4)} Is this relation a function? {(1,-1),(2,0),(3,1),(5,6),(2,4)}

16. x (inputs) y (outputs) -6-9 -5-7 3 24 67 3-7 Find: 1.domain 2.range 3.y if x = -1 4.x if y = 7 f

17. For function f: y = 3 f (-1) = 3 function notation x (inputs) y (outputs) -6-9 -5-7 3 24 67 f “The value at x = -1 is 3.”

18. xf (x) 13 013 1-3 43 65 65 31 Is f (x) a function? Vertical Line Test – as a vertical line passes it never touches more than one point on the graph NO! Graph it!

19. Is g(x) a function? YES! Graph it! g(x) = -3x – 6 f (x) = mx + b linear function

20. Is this a graph of a function? NOT A FUNCTION!

21. Is this a graph of a function? FUNCTION!

22. Evaluating Functions Remember f(x) is just function notation! A. If f(x) = 3x – 4, find f (4). f(4)=3(4) – 4Replace x with 4. =12 – 4Multiply. = 8Subtract. Answer: f (4) = 8

23. B. If f(x) = 3x – 4, find f(–5).

24. C. If h(t) = 1248 – 160t + 16t 2, find h(3).

25. D. If f(x) = 4x+9 Find f(2) f(-3)+7 f(2y) EVALUATING CHALLENGE!!!

26. The function h(t) = 180 – 16t 2 represents the height of a ball thrown from a cliff that is 180 feet above the ground. Find h(2z). APPLICATION CHALLENGE!!!

27. Homework: 1.7 Practice Worksheet (ODDS) Algebra A/B