RELATIONS & FUNCTIONS DICTIONARY

Transcription

1 RELATIONS & FUNCTIONS DICTIONARY Graphing Basics DEFINITION EXAMPLE OR VISUAL Coordinate Plane x-axis y-axis Quadrants Origin Ordered Pair x-coordinate

2 y-coordinate Discrete Graph Continuous Graph Relation Domain Range Mapping Function Function Function Functions DEFINITION EXAMPLE OR VISUAL Function

3 Function Notation Input Output Vertical Line Test Zeros Sequences & Patterns DEFINITION EXAMPLE OR VISUAL Arithmetic Sequence Common Difference Arithmetic Sequence Formula

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9 Name: Date: Bell: Unit : Functions & Linear Equations Homework : Relations & Functions ** This is a -page document! ** Find the domain and range, then represent as a table, mapping, and graph.. {(-5, ), (-, -), (-, ), (0, ), (, )} Domain = Range =. {(-, -), (-, ), (0,0), (-, 5), (, )} Domain = Range = Determine the domain and range of the following continuous graphs... Domain = Range = Domain = Range = Domain = Range = Domain = Range =

10 7. 8. Domain = Range = 9. Domain = Range = 0. Domain = Range = Domain = Range = Determine which of the following relations could represent functions.. {(-, 6), (, 0), (, 6), (, -), (5, )}. {(-, ), (-, ), (, ), (-, ), (0, )} x y. x y

11 Graphing Functions Functions can be represented by an equation. To graph them, you can create a table to plot the points. Example: y = x x - 0 y Directions: Complete the function table, then graph your results.. y = x +. y = x. y = x. y = x + 5. y = -x + 6. y = x

12 Directions: Given the domain, find the range values. 7. y = x 5 Domain = {, 6, 8} 8. y = x + Domain = {-, 0,, } 9. y = x Domain = {-,, 5} 0. y = 5 x + Domain = {-0, 0, 5}. y = 7 x Domain = {-, 0, 6}. y = x + 9 Domain = {-, -6, }

13 x y x y x - 0 y x - 0 y

14 Function Notation Equations can be written in a form called function notation. We use this as a quick way to evaluate functions for a given input. Example: y = x 8 This is read as Evaluating Functions To evaluate a function for a specific value, substitute the value in for. =+ = a. 5 a. b. b. c. c. 0 = = a. h a. b. h0 b. c. h9 c. 7 5 = + 6 = + a. h a. b. h b. c. h0 c. 5

15 7 = + = 8 a. 8 a. h 5 b. b. h c. 0 c. h 9 = + 0 = É É a. 8 a. b. 5 b. 7 c. c. Anthropologists use the length of certain bones of human skeleton to estimate the height of the living person. One of these bones is the femur. To estimate the height in centimeters of a female with a femur length of, the function =.+. can be used. a. Find h6 b. What does this mean? Given the graph of the function f(x), find each of the following. f(x) 5 y a. b x c. d. 5-5

16 Name: Date: Bell: Unit : Relations & Functions Homework : Function Notation & Evaluating Functions. Given =, find the following. a. b. c.. Given = +, find the following. a. b. 0 c. 0. Given = +, find the following. a. h b. h 5 c. h 8. Given =, find the following. a. b. 0 c. 5. Given = +, find the following. a Given =, find the following. a. h b. b. h 7 c. c. h9 7. Given = +, find the following. a. 60 b. 0 c The following represents the graph of a function f(x). Find each of the following O - 5 a. f(-) b. f() c. f(0)

17 Name: Topic: Main Ideas/Questions Notes Date: Class: DEFINITION What are they also called? GIVEN GRAPH

18 Main Ideas/Questions ALGEBRAICALLY (By hand) Notes. f(x) = x 8. f(x) = x + Step :. f(x) = -x + 7. f(x) = x 6 Step : 5. f(x) = x + 6. f(x) = x + 5 BY GRAPHING CALCULATOR Step : Hit Y = to enter the function Step : Hit GRAPH to view the graph.. f(x) = x 6. f(x) = 5x + 5x 0. f(x) = -x x +. f(x) = x + 7x 8 5. f(x) = x x 8 6. f(x) = -x + 7x 0 7. f(x) = x 5x + x f(x) = x + x 5x 9. f(x) = x x 0. f(x) = x + x 5x 50x

19 Name: Date: Bell: Unit : Relations & Functions Homework : Zeros of Functions Directions: Find the zeros of each function given the graph. y. y.. O x O x O y 5 5 x. 5. y O y 5 5 x O x - - O x - - Directions: Find the zeros of each function algebraically. 7. f(x) = x + 8. f(x) = -x f(x) = x 6 0. f(x) = x + 0. f(x) = x +. f(x) = x 5 Directions: Find the zeros of each function by using your graphing calculator.. f(x) = x 6. f(x) = x x 5 5. f(x) = x 5x f(x) = x 6x + x f(x) = x x x + 8. f(x) = x 5x + 0x 6

20 Analyzing Graphs DIRECTIONS: Given the graph below, write a description in words. Use the elements of the vocabulary list below. Be very descriptive as if you were teaching somebody how to analyze the graph. VOCABULARY: DISCRETE OR CONTINUOUS GRAPH, DOMAIN, RANGE, FUNCTION, VERTICAL LINE TEST, ZEROS

21 Name: Topic: Main Ideas/Questions Notes Date: Class: Arithmetic Sequence Common Difference Identifying an Arithmetic Sequence Determine whether the sequences are arithmetic sequences. If yes, identify the common difference.., 5, 9,,.,, 5, 8,. 8, 6,,,. -5, -8, -, -, 5. 5, 0, 0, 0, 6. 7, 6, 5,, Continuing Arithmetic Sequences Given the arithmetic sequence, find the next three terms. 7. 9,, 7,,,, 8. 5,, -, -,,, 9. -8, -,, 0,,, Arithmetic The n th term of an arithmetic sequence can be found using the following formula: Sequence Formula Examples Write the rule for the nth term, then find a 9. d = a = 0. 7,, 9, 5,. 0, 6,, 8,

22 Main Ideas/Questions Notes. -, -8, -5, -. -, 0,,,. -6, -, -6, -, 5. 0, 9, 8, 7, Real Life Applications 6. You visit the Grand Canyon and drop a penny off the edge of the cliff. The distance the penny will fall is 6 feet for the first second,8 feet the next second, 80 feet the third second, and so on. a. Write a formula to represent this sequence. b. How far will the penny have traveled after 6 seconds? 7. The total bank loan for Sarah s new car is $5,65. The bank automatically withdraws $95.80 each month to pay off the car. a. Write a formula to represent this sequence. b. What will be the balance of the loan after years?

23 Name: Date: Bell: Unit : Relations & Functions Homework 5: Arithmetic Sequences & Quiz - Review ** This is a -page document! ** Determine whether each sequence is an arithmetic sequence. If yes, identify the common difference.., 7, 9,,. 5,,, 9,. 7, 0,, 6,. -6, -5, -, -, 5. -, -6,, 8, 6. -9, -, -9, -, Find the next three terms of each arithmetic sequence. 7., 7,, 5,,, 8., 0, 8, 6,,, 9. -, -, -9, -7,,, 0. -, -5, -8, -,,, Write an equation to find the nth term of each sequence. Then find a.,, 5, 7,. -, -, -7, - 0,. -, -9, -, -9,. 7,, 9, 5, 5. Charlie deposited $5 in a savings account. Each week thereafter, he deposits $5 into the account. a. Write a formula to represent this sequence. 6. As manager of the soccer team, Wendy is to hand out cups of water at practice. Each cup of water is ounces. She begins practice with a 8-ounce cooler of water. a. Write a formula to represent this sequence. b. How much total money has Charlie deposited after 0 weeks? b. How much water is remaining after she hands out the th cup?

24 Review! Review! Evaluating functions, and identifying zeros of functions will also be on the quiz.. Given = 8+, find 5. Given = + 9, find. Given h =, find h 8. Given = É9 É, find 7 Use = and = ++ to answer questions Find the zero(s) of the following functions algebraically: a. = b. = + 0. Find the zero(s) of the following functions using your graphing calculator: a. = 7+0 b. = 9 ++

25 Relations Unit Test Study Guide Relations & Functions. {(-6, ), (5, -), (0, ), (-, )}. x y 8-5 a. Domain = b. Range = c. Function? a. Domain = b. Range = c. Function?.. a. Domain = b. Range = c. Function? a. Domain = b. Range = c. Function? 5. y 5 O 5 x a. Domain = b. Range = c. Function? d. Zero(s)? 6. y O x a. Domain = b. Range = c. Function? d. Zero(s)?

26 Graphing Functions 7. y = -x y = x x 0 5 y x - 0 y Function Notation Use =, = +, and = h 8. + Zeros. Find the zero(s) algebraically: =. Find the zero(s) using your graphing calculator: = + + Arithmetic Sequences a n = d(n ) + a 5. Given {5,,, -, }, Find a 8 6. Given {-, 5,, 9, }, Find a