Today’s Topics: Function Notation Domain & Range Recognizing Functions 1.1 Functions and Models Today’s Topics: Function Notation Domain & Range Recognizing Functions

Definition Function: A function is a rule or correspondence that assigns to each element of one set exactly one element of a second set. The function may be defined by a set of ordered pairs, a table, a graph an equation or a verbal description.

Part I – Function Notation Ex 1 – Function Notation with Equations Evaluate the following expressions given the functions below: g(x) = -3x + 1 f(x) = x2 + 7 𝐡 𝐱 = 𝟏𝟐 𝐱 a. g(10) = b. f(3) = c. h(–2) =   d. f(-7) = e. h(4) = f. g(-5) =

Ex 2: Function Notation with a Graph f(x) y x 5 -5 Find:   f(–4) = f(0) = f(3) = f(-5) =

Ex 3: Mortgage Mortgage A couple can afford $800 per month to purchase a home. As indicated in the table, if they can get an interest rate of 7.5%, the number of years that it will take to pay off the mortgage is a function of the dollar amount A of the mortgage for the home they purchase. Amount A ($) t (years) 40,000 5 69,000 10 89,000 15 103,000 20 120,000 30 If the couple wishes to finance $103,000, for how long must they make payments? Write this in function form if t = f(A). What if f(120,000)? Write a sentence that explains its meaning. What is f(3∙40,000)? What value of A makes f(A) = 5 true? Does f(3∙40,000) = 3 ∙ f(40,000)? Explain your reasoning.

Part II – Domain & Range Definition Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work Definition Range: The range is the set of all possible output values (usually y), which result from using the function formula.

Ex 1: Relationship between Celsius and Fahrenheit Celsius Degrees -20 -10 -5 25 50 100 Fahrenheit Degrees -4 14 23 32 77 122 212 Using the table above, determine the domain and the range.

Ex 2: Write the domain and range of each function. D: D: R: R:

Ex. 3: Domain and Range For each of the following functions, determine the domain. Determine the range of each function. y = 𝑥 2 +5 𝑓(𝑥)=2+ 1 2𝑥−5 𝑔(𝑥)= 1 2 7−3𝑥 Determine the domain and range of this function. 𝑥 2 + 𝑦 2 =25

Part III – Recognizing Functions Recall that a function is a rule or correspondence that assigns to each element of one set (called the domain) exactly one element of a second set (called the range). The function may be defined by a set of ordered pairs, a table, a graph, an equation or a verbal description.

Ex. 1: Determine whether or not the indicated relationship represents a function. Y -100 5 109 10 480 15 505 20 25 30 . Does the table describe y as a function of x? Why or why not? Does the equation 𝑦 2 =5𝑥−5 define y as a function of x?

Recognizing Functions Definition Vertical Line Test: A set of points in a coordinate plane is a the graph of a function if and only if no vertical line intersects the graph more than one point. Examples on the white board.

Assignment Pg. 18-23 #3-17 odd #26 #28 #29-33 all #49 #66