{ x + 2 if x < Study Guide and Intervention. Special Functions

Transcription

1 NAME DATE PERID -6 Stud Guide and Intervention Piecewise-Defined Functions A piecewise-defined function is written using two or more epressions. Its graph is often disjointed. Eample Graph f() = if < { - if. First, graph the linear function f() = for <. Since does not satisf this inequalit, stop with a circle at (, ). Net, graph the linear function f() = - for. Since does satisf this inequalit, begin with a dot at (, ). - - f() - - Eercises Graph each function. Identif the domain and range. { + if < 0. f () = + 5 if if >. f () = {- - if < if if > 0 { if 0. h() = - 6 if 0 < < if h() Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 6 Glencoe Algebra

2 NAME DATE PERID -6 Stud Guide and Intervention (continued) Step Functions and Absolute Value Functions Name Written as Graphed as Greatest Integer Function f() = Lesson Absolute Value Function f() = two ras that are mirror images of each other and meet at a point, the verte Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Eample Graph f() = -. Find several ordered pairs. Graph the points and connect them. You would epect the graph to look similar to its parent function, f() =. Eercises Graph each function. Identif the domain and range.. f() =. h() = +. f() = + f() h() f() f() Chapter 7 Glencoe Algebra

3 NAME DATE PERID -6 Skills Practice Graph each function. Identif the domain and range.. f() = { - if 0 - if < - if 0 <. f() = 0 if - { 6 if > if > f() f(). f() = { if < 0. h() = { if 0 f() h() if < - + if > 5. f() = + 6. f() = - f() f() 7. g() = 8. f() = + g() f() Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 8 Glencoe Algebra

4 NAME DATE PERID -6 Practice Graph each function. Identif the domain and range.. f() = { + if -. h() = { - if > 0 if > if < 0 f() h() Lesson -6. f() = 0.5. f() = - f() f() Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 5. g() = - 6. f() = + g() 7. BUSINESS A Stitch in Time charges $0 per hour or an fraction thereof for labor. Draw a graph of the step function that represents this situation. Labor Costs Total Cost ($) Hours Chapter 9 Glencoe Algebra f() 8. BUSINESS A wholesaler charges a store $.00 per pound for less than 0 pounds of cand and $.50 per pound for 0 or more pounds. Draw a graph of the function that represents this situation. Cost ($) Cand Costs Pounds

5 NAME DATE PERID -6 Word Problem Practice. SAVINGS Nathan puts $00 into a checking account as soon as he gets his pacheck. The value of his checking account is modeled b the formula 00m, where m is the number of months that Nathan has been working. After 05 das, how much mone is in the account?. ARCHITECTURE The cross-section of a roof is shown in the figure. Write an absolute value function that models the shape of the roof.. FINANCE A financial advisor handles the transactions for a customer. The median annual earnings for financial advisors is around $60,000. For ever transaction, a certain financial advisor gets a 5% commission, regardless of whether the transaction is a deposit or withdrawal. Write a formula using the absolute value function for the advisor s commission. Let D represent the value of one transaction.. RUNDING A science teacher instructs students to round their measurements as follows: If a number is less than 0.5 of a millimeter, students are instructed to round down. If a number is eactl 0.5 or greater, students are told to round up to the net millimeter. Write a formula that takes a measurement millimeters and ields the rounded off number. 5. GAMES Some oung people are plaing a game where a wooden plank is used as a target. It is marked off into 6 equal parts. A value is written in each section to represent the score earned if the dart lands in that section. Let denote the horizontal position of a dart on the board, where the center of the board is the origin. Negative values correspond to the left half of the dart board, and positive values correspond to the right half. A plaer s score depends on the distance of the dart from the origin. a. Write a formula that gives the horizontal distance from the center of the dartboard. b. Write a formula using the greatest integer function that can be used to find the person s score. Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 0 Glencoe Algebra

6 NAME DATE PERID -6 Enrichment Graphing Greatest Integer Functions Some equations involving the greatest integer function produce interesting graphs. It will be helpful to make a chart of values for each function and to use a colored pen or pencil. Graph each function.. = -. = Lesson Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. = = Chapter Glencoe Algebra

7 NAME DATE PERID -6 Graphing Calculator Activit Transformations: Greatest Integer Function A graphing calculator can be used to displa transformations to the greatest integer function. This is done b using the int( command under the MATH NUM menu. When graphing the greatest integer function, it is important to set the calculator to Dot mode. Eample Graph f() = and g() = + on the same aes. Evaluate each function for = 0.6, =, =., =, = - 0.5, and = -.. Compare the graphs of the functions. Enter f() in Y and g() in Y. Graph the functions. Kestrokes: Y= MATH 5 ) ENTER MATH 5 ) + ENTER ZM 6 ZM. Use TRACE to evaluate each function for the given values. Kestrokes: TRACE 0.6 ENTER ENTER. ENTER ENTER ( ) 0.5 ENTER ( ). ENTER 0.6 ENTER ENTER. ENTER ENTER ( ) 0.5 ENTER ( ). ENTER. f(0.6) = 0, f() =, f(.) =, f() =, f(-0.5) = -, and f(-.) = - g(0.6) =, g() =, g(.) =, g() =, g(-0.5) = -, and g(-.) = 0 [-.7,.7] scl: b [-.,.] scl: The graph of g() = + is the same as the graph of f() = shifted units up. Eercises Graph each function. Evaluate it for =, =., and =. Compare the graph of the function to the graph of f() =.. g() = -. g() = -. g() = +. g() = - 5. g() = 6. g() = Copright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter Glencoe Algebra