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Transcript
FUNCTION NOTATION AND EVALUATING FUNCTIONS SECTIONS 5.1 & 14.1B relation is a set of __________________. ordered pairs A ________ The ________ of ________ numbers domain is the ______ set first in a relation. The ________ is the ______ of ________ range set second numbers in a relation. function A ___________ is a relation in which no number in the domain repeated _________ is __________. Functions can be represented five different ways: mapping 1. ______________ graph 2. ______________ 3. ______________ table Set of ordered pairs 4. ______________ equation 5. ______________ Sometimes we will only know one part of the ordered pair. We can use the equation to find the missing number. Example 1: Complete each ordered pair so that it is a solution to 2 x y 9. a. ( 1, ? ) y x 1 What is ____ if _________? 2x y 9 2 1 y 9 2 y 9 -2 y7 (1, 7) b. ( ?, 9 ) x y 9 What is ____ if _________? 2x y 9 2 x 9 9 -9 2x 0 2 2 x0 (0, 9) TRY THIS…. c. ( 4, ? ) y x4 What is ____ if _________? 2x y 9 2 4 y 9 8 y 9 -8 y 1 (4, 1) Function notation replaces the independent variable, y with either f(x), g(x), or h(x). f _____ of _____” x f(x) is read as “ ____ Does not mean multiplication! g _____ of _____” x g(x) is read as “ ____ h _____ of _____” x h(x) is read as “ ____ Instead of writing, y x3 , we replace the y with f ( x) f ( x) x 3 f of x equals x 3 is read as “ ___________________________________” Function Notation f ( x) x 2 Read as 2 f of x equals x f ( x) x f of x equals the absolute value of x f of x equals the square root of x f ( x) x 2 f ( x) 3 x 2 f of x equals 3 x Look at the mappings below. is happening to What is happening to each number in theWhat domain to get the x to get the corresponding number in the range? Domain Range 2 8 5 11 10 16 x Domain x f ( x) Range f ( x) -3 -6 0 0 5 10 corresponding f(x) value? Function Rule: f ( x) x 6 What is happening to x to get the corresponding f(x) value? Function Rule: f ( x) 2 x function rule can be thought of as an operation that changes the The ______________ numbers in the ___________ to make the ________. domain range f ( x) 3 x 2 4 x 2 Function notation: function rule The right side of any function notation is called the _____________. Replace the y with f(x) Right side of notation Equation Function Notation Function Rule y x6 f ( x) x 6 x6 y 2x2 3 f ( x) 2 x 2 3 2x 3 y 4 x 7 f ( x) 4 x 7 4 x 7 2 input The numbers of the domain are sometimes called the ________ and the output range is called the ___________. Changes the domain into the range x input output Function Rule f ( x) Find the range for the function f ( x) 3 x 1 if the domain of f(x) is { 0, 2, 4 }. domain Range = { 1, 7, 13 3x 1 range Domain 0 3 0 1 1 2 3 2 1 Range 0 1 2 7 4 13 7 4 3 4 1 } Written as ordered pairs: 13 {(0,1), (2, 7), (4,13)} Try this… h( x) x 2 2 For the function, , find the range if the domain is { -3, 0, 4 }. x2 2 Input 3 3 0 0 4 4 Output 2 = 92 7 2 2 = 02 2 2 2 = 16 2 14 2 Range: {2, 7, 14} Sometimes we only want to only evaluate one element of the domain. For example, if g ( x) x 2 3x 1 find g ( x ) when “find g ( x ) when x2 x2 ”, can be written in a shorter form as “ g (2) ”. Example 2: If g ( x) x 3x 1 find 2 g (2) g ( x) x 2 3 x 1 g (2) . 2 3 2 1 2 Plug 2 into the function rule. g (2) 4 6 1 g (2) 1 g (2) 1 If h( x) 2 x 3x 2 2 Try these… find: A. h (0) h(0) 2 0 3 0 2 . 2 h(0) 0 0 2 h(0) 2 B. h (2) h(2) 2 2 3 2 2 . 2 h(2) 2 4 6 2 h(2) 8 6 2 h( 2) 0