2. Aim: What is the function notation? Do Now: 1. y = x + 2, find y when x = 4 2. y = x 2 + 1, find y when x = 2 HW: p.129 # 3,4,7,10,12,14,15 p.126 # 17,19,21

3. We know the graphs of y = x + 2 and y = x 2 +1 are a line and a parabola. We also know both y = x + 2 and y = x 2 +1 are functions We can use different function notations to write them The following are the common function notations: Where the letter can be changed to g, h, or other letters The most common notation is f(x) = ···········

4. Let’s compare two types of notations for the same question from Do Now y = x + 2, f(x) = x + 2 if x = 4 then y = 4 + 2 = 6 f(4) = 4 + 2 = 6 y = x 2 + 1 f(x) = x 2 + 1 If x = 2, y = 2 2 + 1 = 5 f(2) = 2 2 + 1 = 5 From the above examples, we know that y = f(x)

5. Given a function f(x) = 2x + 15, find the value of f(-3) f(-3) = 2(-3) + 15 = -6 + 15 = 9 Given a function g(x) = x 2 – 7, find the value of g(2) g(2) = 2 2 – 7 = 4 – 7 = – 3

6. Let f be the set of ordered pairs such that the second element of each pair is 1 more than twice the first. a.Write f(x) in terms of x. b.Find f(7) c.Find f(-5) a. f(x) = 2x + 1 b. f(7) = 2(7) + 1 = 15 c. f(-5) = 2(-5) + 1 = –9

7. The graph of function f is shown above. Find a. f(-1) b. f(0) c. f(1) d. f(3)

8. The domain of a function is the values of x’s that will well defined the function

9. Find the domain of the following functions: 1. 2. 3. 4.

10. Students will be able to 1. use function notation to evaluate functions for given values in the domain 2. find the domain and range of a function 3. write functions in functional notation 4. evaluate functions using function notation given a numerical or an algebraic input 5. determine if a function is one-to-one, onto, or both

11. Observe and explain patterns to formulate generalizations and conjectures Use multiple representations to represent and explain problem situations Use a variety of strategies to extend solution methods to other problems Investigate and evaluate conjectures in mathematical terms, using mathematical strategies to reach a conclusion Develop, verify, and explain an argument, using appropriate mathematical ideas and language Performance Standard