0//0 MATH COLLEGE ALGEBRA AND TRIGONOMETRY UNIT HOMEWORK ASSIGNMENTS General Instructions Be sure to write out all our work, because method is as important as getting the correct answer. The answers to the odd-numbered problems are in the back of the book, beginning on page. The answers to the even-numbered problems and to the Additional Problems are at the end of this handout. CHAPTER Section. Function and Function Notation Tet, page :,,,, 7,,,, 9, Section. Rate of Change A. Tet, page : b, 9,,, B. Additional Problems:. The graph of f ( ) is at the right. a. On what interval is the graph increasing? b. On what interval is the graph decreasing? 0. The graph of f ( ) is at the right. a. On what intervals is the graph increasing? b. On what intervals is the graph decreasing? Section. Linear Functions A. Tet, page :,,, 7, 9,,, 9,, 7, 9 B. Appendi F, page :, 9 Section. Formulas for Linear Functions Tet, page 0:,,, 0, 7,,, 7, 9,
Section. Geometric Properties of Linear Functions A.. Tet, page 9:,,, 7, 9,,, 9,,,,, 9. Appendi G, page 9:,, 7, 9,. Check our answer b graphing both equations on our calculator. Then use ND CALC, : INTERSECT to find the point of intersection. B. Additional Problems:. Write the equation of the line that is parallel to = and contains the point (, ).. Write the equation of the line that is parallel to = and contains the point (, ).. Write the equation of the line that is perpendicular to the line = and contains the point (, ).. Write the equation of the line that is perpendicular to the line + = 0 and contains the point (, ).. Write the equation of a line parallel to the line + =.. Write the equation of a line perpendicular to the line = 9. 7. Write the equations of two lines that contain the point (, ).. Each of the equations below represents the population of animals in a certain region, where t is the ear. Describe in words what each of the equations tells ou about the population of animals. a. P = 70 + t b. P = 00 0 t c. P = 0t + 900 d. Which population starts out with the most animals? Which population is growing fastest? CHAPTER A. Appendi B, page :, Appendi F, page :,,,, 9 B. Additional Problems: Simplif each comple fraction b multipling the numerator and denominator b the LCD: 9 +... + + Section. Input and Output Tet, page :,,, 7, 9, 0,, a-b,, 9, (use calculator), Section. Domain and Range A. Tet, page 0:,,, 9,, 9,,, 7 Continued on net page
B. Additional Problems:. Consider the graph at right. a. Does the graph represent a function? b. Assuming the graph is complete, what is the domain? c. Assuming the graph is complete, what is the range? d. On what intervals is the function increasing? Decreasing?. Suppose f ( ) =. a. State the domain. b. Algebraicall, find the -intercepts. c. Find the -intercept. d. Use our calculator to graph the function. You will need to determine a suitable. window. Draw our graph and label our scale. e. Find the range algebraicall. (Hint: Use what ou know about parabolas and review the formula for the verte.) Does this range agree with the graph? f. On what intervals is the function increasing? Decreasing?. Suppose g ( ) = 9 a. Find the domain algebraicall. b. Algebraicall, find the -intercepts. c. Find the -intercept. d. Use our calculator to graph the function. You will need to determine a suitable window. Draw our graph and label our scale. e. From the graph, what is the range? f. On what intervals is the function increasing? Decreasing?. Suppose = h( ) = ( ) + a. Find h( 0 ) b. Find all values of for which h c. Find h(. ) d. What are the -intercepts? e. What is the -intercept? f. What is the domain? ( ) = 0.. Find the domain of f ( ) =. Show our steps do not use a graph.. Find the domain of =. Show our steps do not use a graph. +
Section. Piecewise Defined Functions A. Librar of Functions For each function listed below, provide a graph with important points and features labeled. State: domain, range, intercepts, and the intervals where the function is increasing and decreasing.. =. =. =. =. =. = B. Tet, page :,, 7, 9,, C. Additional Problems:. a. Graph the piecewise function given b f( ) = b. State the range of the function. c. State the intercepts. d. On what intervals is the function increasing? Decreasing? < 0. Given f( ) = 0 > a. Find f ( ) b. Find f ( 0 ) c. Find f ( 0.) > d. Find f ( ) e. Find f ( ) f. Graph the function. g. State the range. h. What are the intercepts? i. On what intervals is the function increasing? Decreasing?. The graph of the piecewise function g is given. The domain of g is. a. What is the range of g? b. What are the intercepts? c. Write a formula for g.
Section. Concavit A. Tet, page 9:,,, 7, 9,,, 7 B. Additional problems:. The graph of f ( ) is at the right. a. On what intervals is the graph increasing? b. On what intervals is the graph decreasing? c. On what intervals is the graph concave up? d. On what intervals is the graph concave down?. The graph of f ( ) is at the right. a. Approimate the intervals where the graph is concave up. b. Approimate the intervals where the graph is concave down. Section. Vertical and Horizontal Shifts A.. Tet, page 77: a, c, 9, 7,,, 9 B. Additional Problems: For Problems, state the basic function, state the transformations, and sketch the graph b hand, showing intercepts, where the origin moved, and/or asmptotes where appropriate. Check our graph b using our calculator.. f ( ) = ( ) + (Also epand this function and write in standard form.). = + (Also, epress this function as a single fraction.) +. h ( ) = ( + ). = + Continued on net page
For problems 7, a graph is given. State the basic function, state the transformations, and write the equation of the transformed function... 7 9 ` 7. 7 Section. Reflections and Smmetr A. Tet, page :,, 9, 9,,,, 7, 9a, b,, 7, 9. B. Additional Problems: For the functions in problems - : State the basic function with transformations, and sketch the graph b hand, showing important points and/or asmptotes where appropriate. Check our graph b using our calculator.. f ( )=. g ( ) = +. =. = + +. = + c h Continued on net page
For the functions in problems : State the basic function with transformations, and write a formula for the new function.. 7. 9. 7
Answers to Even-numbered and Additional Problems. f (0) = 0. f () = 0. Horizontal Ais: t ( ears) Vertical Ais: P(millions). a. 9 F b. Jul 7 th and Jul 0 th c. Yes, for each date there is eactl one temperature. d. No, it is not true that for each temperature there is eactl one date.. B. a. (0, ) b. (, 0). a. (,0) (, ) b. (, ) (0,).A. P =, 0 + t. a. = 00 + 0 b. If =$,000, then = 00 If =$ 0,000, then = 00 c. If =700, then = 00,000 The firm would need to spend $00,000 to sell 700 units. d. Slope = 0. For each etra $ spent on advertising, 0 of a unit etra is sold, or for each etra $0 spent, more unit sold..b. 7 = 9. 0 t = 7. 0. = +. = +. = +.A. =. (,) and (, ) ;.A. (, ). (, ) 7. (, ) or (, ) 9., or,., = +. B. = +. = + or =. =. =. There are man answers; each line must have the same slope. m =. There are man answers; each line must have the same slope. m = 7. There are man answers. Some are: + = ; = ; =. a. Initiall (in ear 0), the population was 70 and it is increasing b animals per ear. b. Initiall (in ear 0), the population was 00 and it is decreasing b 0 animals per ear. c. Initiall (in ear 0), the population was 900 and it is increasing b 0 animals per ear.
d. Population (c) starts with the most animals (the P-intercept of the equation is largest), while Population (a) grows the fastest (the equation has the largest slope). Chapter A Appendi B. + 0. + Appendi F. w =., w =. t = 0, t =, t =.,. w =. 9. =, = Chapter B 9 ( )(+ ) +. = = ( ).. +. 0. a. g (0) = b. t =. a. b. g( ) = 9 g( ) = ( ) + ( ) = +. a. h () = feet h () = feet The height of the ball is feet after second and after seconds. b. The ball hits the ground after seconds. The maimum height is feet.. B. a. The graph represents a function because it passes the vertical line test. b. The domain is [, ] c. The range is [, ) d. The graph is increasing on (0, ) and decreasing on (, ) (, 0) (, ).. a. The domain is all real numbers. Ever value produces a value. b. = 0 ( )( + ) = 0 = or = The -intercepts are and. c. The -intercept is. d. A good window is: Xmin =, Xma =, Ymin =, Yma = 0 0 e. Because the verte is (.,.), the range is [., ) f. f is increasing on (0., ) and decreasing on (, 0.).. a. The denominator cannot be zero. 9 = 0 ( + )( ) = 0 = or = The domain is all real numbers ecept and. OR: The domain is (, ) (, ) (, ). 9
b. = 0 9 = 0 The -intercept is 0. c. The -intercept is 0. See front book cover..c. a. d. A good window is: Xmin =, Xma =, Ymin =, Yma = e. The range is all real numbers. f. g is never increasing; g is deceasing on (, ) (, ) (, ).. a. h (0) = b. h ( ) = 0 ( ) = 0 + ( ) = 0 = Thus, h ( ) = 0 if =. c. h () = 0 (see (b)) d. The -intercept of h is (see (b)) e. The -intercept of h is (see (a)). f. (, ). Domain: 0, (,]..A 0 Domain: (, ) + > 0 > > b. The range is all real numbers. c. The -intercept is 0 The -intercept is 0. d. The function is increasing on (, ). The function is never decreasing. f =. a. ( ) b. f ( 0) = c. f ( 0.) =. d. f ( ) = e. f ( ) = f. g. The range is (,0 ) [,] (, ). h. The -intercept is ; there is no - intercept. 7 i. The function is increasing on (, ) and decreasing on (,0) (0, ). a. The range is { } [0,) { }. 0
b. The -intercept is 0; the -intercept is 0. < 0 c. g( ) = 0 <. A. This is an increasing function because as time increases more drug is injected into the bod. The graph is concave down because the rate of increase slows down.. B. a. never increasing. b. (, ) (, ) (, ) c. (,0) (, ) d. (, ) (0,). = + Basic function: = Shift right ; shift up.. Basic function: = Shift left ; shift down Equation: ( ) = +. Basic function: = Shift right Equation: = 7. Basic function: Shift up Equation: = = +. a. Concave up:. B (, 0.) ( 0., ) b. Concave down: ( 0.,0) ( 0, 0.). A. a. = + Note: For problems, check our graphs b using our graphing calculator.... f( ) = ( ) + = Basic function: = Shift right ; shift up = + = + 9 + + Basic function; = Shift left ; shift up h( ) = ( + ) = + + 7+ Basic function: = Shift left ; shift down + 0 b. = ( + ) c. Not the same.
. a. The building is kept at 0 F until a.m. when the heat is turned up. The building heats up at a constant rate until 7 am when is F. It stas at that temperature until pm when the heat is turned down. The building cools at a constant rate until pm. At that time the temperature is 0 F and stas at that level through the end of the da. b.. = Basic function: = Reflect across -ais; reflect across -ais.. = + + Basic function: = Shift left ; reflect across -ais; shift up.. ( ) = + = Basic function: = Shift right ; reflect across -ais; shift down. or shift right ; shift up ; reflect across -ais.. Basic function: = Reflect across -ais; shift up. Equation: = + 0 c. This could describe the cooling schedule in the summer months when the temperature is kept at F at night and cooled down to 7 during the da.. The function will be decreasing and concave down in the second quadrant.. B Note: For problems, check our graphs using our graphing calculator... f( ) = Basic function: = Reflect across -ais; shift down g( ) = + Basic function: = Shift left ; reflect across -ais. 7. Basic function: = Note that in this function there are two inside changes: Reflect across -ais; shift left. The reflection produces the new function =. Shifting that function units to the left requires replacing b +, so our = + or new equation is ( ) =.. Basic function: = Shift right ; reflect across -ais; shift up. Equation: = +