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1 .1 Functions and Models

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.

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1 .1 Functions and Models

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  1. 1.1 Functions and Models Today’s Topics: Function Notation Domain & Range Recognizing Functions

  2. 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.

  3. 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 a.g(10) = b.f(3) = c.h(–2) = d. f(-7) = e. h(4) =f. g(-5) =

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

  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. 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.

  6. 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.

  7. Ex 1: Write the domain and range of each function. D: D: R: R:

  8. Ex. 2: Domain and Range • For each of the following functions, determine the domain. Determine the range of each function. • y = • Determine the domain and range of this function.

  9. Part III – Recognizing Functions Recall that a function is a rule or correspondence that determines exactly one output for each input.

  10. Ex. 1: Determine whether or not the indicated relationship represents a function. • . • Does the equation define y as a function of x?

  11. 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.

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

  13. Ex. 1: Determine whether or not the indicated relationship represents a function. • . Recall that a function is a rule or correspondence that determines exactly one output for each input. YES NO

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