CHAPTER 3 Graphs and Functions

Transcription

1 CHAPTER Graphs and Functions Section. The Rectangular Coordinate Sstem Section. Graphs of Equations Section. Slope and Graphs of Linear Equations Section. Equations of Lines Section. Graphs of Linear Inequalities Section. Relations and Functions Section.7 Graphs of Functions Review Eercises

2 CHAPTER Graphs and Functions Section. Solutions to Even-Numbered Eercises The Rectangular Coordinate Sstem., ), ), ), is units to the left of the vertical ais and units above the horizontal ais., is units to the left of the vertical ais and units below the horizontal ais., is units to the right of the vertical ais and units above the horizontal ais.. 0, ) 0, is 0 units right or left of the vertical ais and units above the horizontal ais. 0, 0 is the origin. 0, 0), 0), 0 is units to the right of the vertical ais and 0 units above or below the horizontal ais.., 7,, is units to the left of the vertical ais and units above the horizontal ais.,, is units to the right of the vertical ais and units below the horizontal ais. is units to the left of the vertical ais and units below the horizontal ais., 7 7., ) 9, ),, is units to the left of the vertical ais and units below the horizontal ais. 9, 9 is units to the right of the vertical ais and units above the horizontal ais., is units to the right of the vertical ais and units below the horizontal ais. 0. Point Position Coordinates A left, above, B right, below, C left, below,. Point Position Coordinates A B C 7 left, below right, above 0 right or left, above 7,, 0,

3 Chapter Graphs and Functions., 7), ) 9, ) 7, 0) 0. 0, 9), ) 0, ) 0., ) 0, ), ), ) 0. 0, 0). Point 0 units right of -ais and units below -ais 0,.. Point units right of -ais and units above -ais,., ), ), ). Coordinates of point are equal in magnitude and opposite in sign and point is 7 units right of -ais 7, 7.. Point is on negative -ais units from the origin 0,. 0., is in Quadrant IV.., is in Quadrant I...,.0 is in Quadrant II..,, > 0, > 0 is in. 0, is in Quadrant I or IV. 0., is in Quadrant III or IV. Quadrant I..,, < 0 is in Quadrant II or IV.. Net sales in billions of dollars) Time in ears). Fuel efficienc in miles per gallon) Speed in miles per hour)., shifted units right and units down,, shifted units right and units down,, shifted units right and units down,, shifted units right and units down, The relationship between and is as the value of increases the value of decreases.

4 Section. The Rectangular Coordinate Sstem ,, 0, ), 0, 9 0, 9) 0, 9) 0, 9) 0, ) 7, ) Kestrokes: Y X,T, X,T, GRAPH. a) 0, b), c), d) 7, 0??? 7? 0?? 9?? 0 Not a solution Not a solution Not a solution Solution. 0 0 a) 0, 0 b), 0 0 0? 0 0? ? 0 0 0? Solution Not a solution c) 0, 0 0? ? Solution d) 0, 0 0? ? 0 0 Not a solution

5 Chapter Graphs and Functions 0. a) 0, 0 b), 0? 0? 0? 0? 0 Not a solution Solution c), 7 7? 7? 0 7 Not a solution d),?? Not a solution. d. 7 7, ), ) Vertical line. d Horizontal line d , ) 0, ) Horizontal line 7 7,, d 0, 0 Vertical line, d d d 0 9

6 Section. The Rectangular Coordinate Sstem 7. d d 0. d 0 0, 9) d 9, ) d, ) 0? 0 d d 9 9 d ? B Pthagorean Theorem, it is a right triangle.., ) d, ) d d, )? 0 d 9 d 9 d 0? B Pthagorean Theorem, it is a right triangle.. d 9 d 9 d 9 9 Not collinear. d 9 0 d d Collinear. d d d P.

7 Chapter Graphs and Functions 90. M 7,, 0, 0 9. M 9 7,,, 7, ), 0), ) 0, 7), 9, ) The emploee s weekl pa is at least $00, and increases $ for ever overtime hour d let,, and, 0, d ards 9. There is a strong relationship between the temperature outside and the amount of natural gas used. The relationship is the lower the temperature the more natural gas used. A famil can epect to use about 00 cubic feet of natural gas if the tempertaure is. 00. let, 000, $,9 and, 00, $9,97 Midpoint ,09 00,,0. Revenue in 00 is $,0. million.,9 9,97 0. The -coordinate measures the distance from the -ais to the point. The -coordinate measures the distance from the -ais to the point. 0., is not a solution point of because 0. The Pthagorean Theorem states that, for a right triangle with hpotenuse c and sides a and b, a b c.

8 Section. Graphs of Equations 7 0. When the sign of the -coordinate is changed, the point is on the opposite side of the -ais as the original point., ) 7, ), ), ), ) 7, ) Section. Graphs of Equations.. Matches graph b). Matches graph a) Matches graph c). 0 0 Solution,, 0, 0,, Solution, 9, 0, 7,, Solution,, 0,,, Solution,,. 0,, 0.,

9 Chapter Graphs and Functions. 0 0 Solution,, 0, 0,, Solution, 0, 0,,, Solution,, 0, 0, 0,. 0 0 Solution,, 0,, 0,. 0 0 Solution,, 0, 0,,

10 Section. Graphs of Equations Solution,, 0 0,, 0,. 0 0 Solution,, 0,, 0, Solution,, 0, 0,,.. -intercept: 0 -intercept: 0 -intercept: 0, 0, 0 -intercept: 0 0, 0 0, intercept: 0 -intercept: , 0, -intercept: 0 0 -intercept: 0 0, 0, 0

11 70 Chapter Graphs and Functions 0.. -intercept: 0 -intercept: 0 -intercept: 0, 0 -intercept: 0, 0 0 None, 0. -intercept: 0 0, -intercept: 0 or, 0,, Estimate: -intercept 9 Check: intercept , 9, 0. Estimate: -intercept 0 Check: 0 0 -intercepts 0, , , 0,, 0 0. Estimate: no -intercept Check: 0 -intercept, 0

12 Section. Graphs of Equations 7. 0 Kestrokes: Y X,T, 0 GRAPH Estimate: -intercept 0, -intercept Check: Check: , , 0. Kestrokes: Y X,T, X,T, GRAPH Estimate: -intercept, -intercepts, 0 0 Check: Check: 0 0 0, 0, 0,, 0. Kestrokes: Y ABS X,T, GRAPH Estimate: -intercept, no -intercepts Check: 0 0, Check: 0 None ,, 0,, 0), ) 0, ) 0, , 0, ), ), 0),

13 7 Chapter Graphs and Functions , 0 0,,, 0), ) 0, ) ,, 0, 9 0, ) 9,, 0) , 0, 0, 0), ) 0 0, 0) or , 9), 0 or, 0 0, 9 0 0,, 0), 0) , 0 ±, 0,, 0, 0), 0) 0, ) or, ) 0, 0 0, 0,, 0,, 0) 0, 0)

14 Section. Graphs of Equations 7 7., 0 0 0,,, ) 7. 0, ), ) 0, 0 0 0,, 7 0, ), ), 0) ,,, 0, ), ), ) 0. 0, t 0, ,000 0, 0,000 0, , 000 Value in dollars) 0,000,000 0,000,000 Time in ears) t. 0 t 0. a) 0,,000, 0, 0,000 m,000 0, t,000, Total assets in billions of dollars) A 7 90 Year 99) t Value in dollars) 0,000 0,000 0,000 0,000 0,000 0,000 b) The model is a good representation of the data because the data points differ onl slightl from the model. c) A 0.t 77 0 Time in ears) t A A 0 77 A $7 billion

15 7 Chapter Graphs and Functions. = +. There are an infinite number of solution points that make up the graph of. = + ) When the epression for is multiplied b, the graph is reflected in the -ais. Additional Eample: and 90. To find the -intercepts, let 0 and solve the equation for. To find the -intercepts, let 0 and solve the equation for. Eample: 0 0, 0 0, -intercept -intercept Section. Slope and Graphs of Linear Equations. 0, and,., 0 and, m 0 m 0. 0, and, m a) m L b) m is undefined L c) m L 0 0. m Line rises. 0. m 0 Line falls. 0 0, 0), ), ) 0, 0)

16 Section. Slope and Graphs of Linear Equations 7. m Line is vertical. 0 undefined 0. m 0 Line rises. 0, ),, ),. m Line rises.. m Line is horizontal , ) 7 9, ) 9, ), ). m Line rises m 0 Line is vertical... undefined 0,,., )., 0). 0, ) 0 Solution, 0,,, ) m 0

17 7 Chapter Graphs and Functions. 0., ), 0 0, ) 0, ) 0 0 Solution, 0,, Solution, 0,, m m is not possible Vertical line:,,,,, An point with an -coordinate of Let 0, solve for : Let, solve for : Let, solve for : Let 0, solve for : 0 0,,, 0, 0

18 Section. Slope and Graphs of Linear Equations 77. Let, solve for : Let 7, solve for :., 7, m 0, m ; 0, 0 m ; 0, slope -intercept 0 slope -intercept 0 0, 0) 0, )

19 7 Chapter Graphs and Functions slope -intercept slope -intercept 0, ) 0, slope -intercept, ) Locate a second point with the slope of. 0, ) m change in change in ,, ) 0 0, 0 Locate a second point with the slope of 0. Line is horizontal., 0) 0, )

20 Section. Slope and Graphs of Linear Equations ,, 0 L : L : m and m m m so the lines are parallel., 0) 0, ) 7. L : 0. L : m and m m m so the lines are perpendicular. L : m L : m 0 m m nor m m so the lines are neither parallel nor perpendicular.. L : m L : m. 0 m m so the lines are perpendicular. 0 0 feet c feet. h h feet

21 0 Chapter Graphs and Functions. a) $,000 $,00 $9, $9,00 $0,00 $,000 t 0 $,000 $,00 $9,00 $9,00 $0,00 $,000 b) Account balance in dollars),000,000 0,000,000 Time in ears) t c) average rate of change $,000 $,000 0,000 $ Yes, an pair of points on a line can be used to calculate the slope of the line. When different pairs of points are selected, the change in and the change in are the lengths of the sides of similar triangles. Corresponding sides of similar triangles are proportional. 9. The line with slope is steeper. There is a vertical change of units for each unit change in. The slope means that there is a vertical change of units for ever unit change in. 9. The -coordinate of the -intercept is the same as the solution of the equation when 0. Section. Equations of Lines.. Matches graph c) Matches graph d) or 9 7 or

22 Section. Equations of Lines or 0 0. m m m. m m. m

23 Chapter Graphs and Functions 0. m m m m 0. because ever 0. because ever. because both points -coordinate is. -coordinate is. have a -coordinate of.. slope a) b) 7. 0 slope 0 a) 0 b)

24 Section. Equations of Lines. 0 slope a) 0 b) slope a) 9 b) The slope is undefined because the line is vertical. a) b) 0 0..

25 Chapter Graphs and Functions. m m 0,000 0,000 00,000 0,000 C F 9 C 0 F 9 9 C 0 F S 0,000 0,000t S 0,000 0,000t 0,000 S 0,000t S 0,000 S $00,000 C 0 F 9 9 C C C. 7. m C 0. 0 C 0. 7 C 0. The sales representative is reimbursed $0. per mile. 7. a) b) C C C 0. 0 C $ estimate $0.0 c) estimate miles miles 7. a) 0, $7,00, $,000 b) V 00 7,00 m,000 7,00 0,00 V 7,00 00t 0 00 V 00 7,00 V $,00 V 00t 7,00

26 Section. Equations of Lines 7. a) 0.0, 000, 000 b) 0,000.0,000 m ,000p , ,000p 0,000,000, Thus, if the price is $.0, the demand will be 000 cans. 0,000p,000 c) 0, , , Thus, if the price is $0.90, the demand will be 000 cans. 0. a) and b) Average test score Average quiz score d) c) Answers will var. Two points taken from the best-fitting line sketched in part b) are, 7 and 0, 99. m m 0 0 Distance from the tall end 0 9 Height of block 0 a) b) c) 0 0 d) e) 9. Yes. When different pairs of points are selected, the change in and the change in are the lengths of the sides of similar triangles. Corresponding sides of similar triangles are proportional.. In the equation, is the slope and is the -intercept.

27 Chapter Graphs and Functions Section. Graphs of Linear Inequalities. < a) c) 0 <? < 0, is not a solution. 0 <? < 0, is a solution. b) 0 <? <, 0 is not a solution. d) <? <, is a solution.. a) c)? 0?, is a solution. 0 0? 0 0? 0 0, 0 is not a solution. b) 0? 0? 0, is a solution. d)? 9?, is a solution.. <. 7 a) c) <?. 7 <?. 7 <., is not a solution. <?. 7 <?. 7 < 0., is a solution. b) <?. 7 d) <? 7. 7 < 0., is not a solution. <?.0 7 <? 0 7 < 7 0, is a solution.. a) 0? 0 0? 0 0, 0 is not a solution. c) 0? 0? 0, 0 is a solution. b)??, is a solution. d)??, is not a solution.

28 Section. Graphs of Linear Inequalities 7 0. < ; a). > 0; e). ; c). <. > 0.. > >. 7 > 00 7 > 00 < <. 0 0

29 Chapter Graphs and Functions Kestrokes: Kestrokes: DRAW 7 0, 9. X,T, ENTER Y X,T, 0 DRAW 7 Y-VARS, 0 ENTER Y X,T, DRAW 7 0, X,T, ENTER DRAW 7 0 Y-VARS, ENTER m 0 0. <. m 0 0 < 0 < < 0 < 0 < < 0 <. P Note: and cannot be negative.) Kestrokes: Note: and cannot be negative.) Y X,T, 0 DRAW 7 Y-VARS, ENTER Number of filing cabinets Number of desks

30 Section. Graphs of Linear Inequalities 9 Cost of Cost for Cost for. a) Verbal Model: cheese etra drinks pizzas toppings Labels: Inequalit: Cost of cheese pizzas 9 $7 Cost for etra toppings.00 dollars) Cost for drinks.0 dollars) b) Note: and cannot be negative.) Number of drinks 0 0 c),.?? es 0 0 Number of toppings 0. a) b) Note: and cannot be negative.) Units of food Y Units of food X, :,,, 9,, 0 Note: and cannot be negative.) Here are some eamples of ordered pairs that are solutions. Note that there are other correct answers.,, 0,,, Time providing childcare in hours) Time at cand store in hours). r 0.70 A., is a solution of a linear inequalit in and means r the inequalit is true when and are substituted for and respectivel. Maimum heart rate in beats per minute) Age in ears) A

31 90 Chapter Graphs and Functions. The solution of > does not include the points on the line. The solution of does include the points on the line. 70. On the real number line, the solution of is an unbounded interval. On a rectangular coordinate sstem, the solution of is a half-plane. Section. Relations and Functions. Domain,,, Range,,, 0. Domain Range,, 0, 0), ), ), ), ), ) 0, )., 0, 0, 00, 7., 0,, 0.,, 0, 0,,,,,, 7,, 0. 9, Reagan, 9, Reagan, 99, G. Bush, 99, Clinton, 997, Clinton, 00, G.W. Bush. Yes, this relation is a function because each element in the domain is assigned eactl one element in the range.. No, this relation is not a function as 00 in the domain is paired with two numbers in the range and 0.. Yes, this relation is a function as each number in the domain is paired with eactl one number in the range.. Yes, this relation is a function because each element in the domain is assigned eactl one element in the range. 0. No, this relation is not a function as 0 in the domain is paired with two numbers in the range and 0 as is and.. Yes, this relation is a function as each number in the domain is paired with eactl one number in the range.. a) No b) Yes c) No d) Yes.. 0? 0? Both 0, and 0, are solutions of which implies is not a function of.? 0? Both, and, 0 are solutions of which implies is not a function of. 0. represents as a function of because there is one value of associated with each value of represents as a function of because there is one value of associated with each value of.

32 Section. Relations and Functions 9. represents as a function of because there is one value of associated with each value of.. f. a) f 0 b) f c) f n n d) f n n n 0 n f a) b) c) f 9 f f h h d) f h h h 0. f a) b) c) 7 f 7 f 7 0 f t t t 7 d) f t t t 0 t 7 t. f 7 a) b) c) f f f t f 7t 7 7t 7t 0 d) f t 7t t t. h a) h 0 b) h c) h h d) ht t t t t. h a) h b) h c) hn n n d) hn n n n

33 9 Chapter Graphs and Functions. g a) b) c) d) g g 0 0 g g g 0. f a) f b) f 9 c) f f 0 d) f. f, if 0, if > 0 a) f b) c) d) f f f f 7 7. f, if <, if a) f 0 b) f c) f 0 d) f f f a) f f f f 9 b) 0. The domain of f is all real numbers.

34 Section. Relations and Functions 9 s 0. The domain if gs is all real numbers s such that s, 0 because s s 0 0 means s 0 s s 0 and s and s 0 0 and s 0.. The domain of f is all real numbers such that because 0 means and.. The domain of G is all real numbers such that because 0 means and.. The domain of f is all real numbers.. Domain:,,, Range: 0,,,,, 70. Domain: Range:,,, 7 7. Domain: all real numbers such that s > 0 Range: all real numbers such that A > 0 7. Domain: all real numbers such that r > 0 Range: all real numbers such that V > 0 7. Verbal Model: Surface Length of edge 7. Verbal Model: Length of diagonal Length of side Labels: Surface S Labels: Length of diagonal L Length of edge Length of side Function: S Function: L 0. Verbal Model: Distance Rate Time. Verbal Model: Distance Rate Time Labels: Distance dt Labels: Distance ds Rate 0 Rate s Time t Time Function: dt 0t Function: ds s. Verbal Model: Labels: Function: Distance Rate Distance ds Rate s Time ds s d 0 miles Time. Verbal Model: Area Side Side Label: Area A Function: A. a) b) P $700 P $70 Wa h, h 0 0, a) W0 0 $0 W0 0 $0 0 < h 0 h > 0 W $70 W $0 b) No. h < 0 is not in the domain of W.

35 9 Chapter Graphs and Functions 9. f 999 7,000,000 7,000,000 students 9. A relation is an set of ordered pairs. A function is a relation in which no two ordered pairs have the same first component and different second components. 9. The domain is the set of inputs of the function and the range is the set of outputs of the function. 9. You can name the function f, g, etc., which is convenient when more than one function is used in solving a problem. The values of the independent and the dependent variables are easil seen in function notation. 00. a) This is not a correct mathematical use of the word function. b) This is a correct mathematical use of the word function. Section.7 Graphs of Functions... Domain: < < Range: < < Domain: < < Range:, or < Domain: < < Range:, or <. 0.. Domain: < < Domain: 0 < Domain:, or < Range:, or < Range: < or, Range: 0, or 0 <... Domain: < < Range: Domain: < < Range: < < Domain: < < Range: 0 < or 0,

36 Section.7 Graphs of Functions t 9 Domain: < t < Range:, or < Domain: or, Range: 0 or 0, Domain: 0 or 0, Range: 0 9 or f) 0 f) 0. h) h) Domain: < < Range:, or < Domain: < < Range: < < 0. Kestrokes:. Kestrokes: Y X,T, GRAPH Y X,T, GRAPH > Domain: < < Domain:, or Range: < Range: 0, or Yes, passes the Vertical Line Test and is a function of.. No, is not a function of b the Vertical Line Test.. No, is not a function of b the Vertical Line Test. 0.. is a function of. is not a function of.

37 9 Chapter Graphs and Functions. d) graph matches f. c) graph matches f. a) Vertical shift units upward b) Vertical shift units downward c) Horizontal shift units to the right d) Horizontal shift units to the left e) Reflection in the -ais followed b a horizontal shift unit to the right followed b a vertical shift units upward f ) Reflection in the -ais 0... Horizontal shift units to the left Reflection in the -ais Reflection in the -ais and vertical shift units upward

38 Section.7 Graphs of Functions 97. Graph is shifted units upward h. Graph is reflected in the -ais and shifted unit upward h 0. Graph is reflected in the -ais and shifted units downward h. h. h. h Graph is shifted unit upward Graph is shifted units right Graph is shifted unit right and reflected across the -ais. f Kestrokes: Y X,T, GRAPH b) f Kestrokes: Y X,T, GRAPH d) f Kestrokes: Y X,T, GRAPH a) f Kestrokes: Y X,T, GRAPH c) f Kestrokes: Y X,T, GRAPH c) a) d) 9 9 b) f) = Basic function: 7. Basic function: c, where c is an constant Transformation: Vertical shift units upward Transformation: Vertical shift 7 units upward Equation of graphed function: Equation of graphed function: 7 7. Basic function: Transformation: Reflection in the - or -ais and a vertical shift unit upward Equation of graphed function: or 7. a) f b) f, ) 0, ), ), ), ), ) 0, 0), ) CONTINUED

39 9 Chapter Graphs and Functions 7. CONTINUED c) f d) f, ), ), 0), ), 0), ) 0, ), ) e) f f ), ) 0, ) f, ) 0, ), 0), ), ), ) 7. Kestrokes: Y.7 X,T, 00 X,T, 0 AND X,T, 000 GRAPH a) b) c)

40 Review Eercises for Chapter a) Verbal Model: Perimeter Length Width Width of walkwa Labels: Perimeter P Length 0 ft Width 0 ft Width of walkwa Function: P P 0 b) Kestrokes: Y 0 X,T, GRAPH c) Slope so for each -foot increase in the width of the walkwa the perimeter increases b feet.. a) T is a function of t because to each time t there corresponds one and onl one temperature T. b) T 0, T 7 c) If the thermostat were reprogrammed to produce a temperature H where Ht Tt, all the temperature changes would occur hour later. d) If the thermostat were reprogrammed to produce a temperature Ht Tt, the temperature would be decreased b degree.. Use the Vertical Line Test to determine if an equation represents as a function of. If the graph of an equation has the propert that no vertical line intersects the graph at two or more) points, the equation represents as a function of.. g fis a reflection in the -ais of the. g f is a horizontal shift units to the graph of f. right of the graph of f. Review Eercises for Chapter., 0) 0,,., ) 0, 0) 7, ) 7, ). Quadrant III. Quadrant I or III

41 00 Chapter Graphs and Functions 0. a), 0 0? 0 b) 0, 9 0 9? 0 9 0? 0 0? no 0 0 es c),? 0 d), 0 0? 0? 0 0? es 0 no. d 0, ), ). d 0 9, 0) 0, ). let A, 7, B,, C, AB 7 BC AC 7 not collinear. Midpoint,,, 0. Midpoint, 7, , 0 0, 0, ), 0

42 Review Eercises for Chapter , 0, 0) 0, ) 0,. 0 0, 0 0, ), ) 0, 0, 0). 0 0, 0 0, 0 0, ), 0), ) intercept: -intercept: , , 0 0 0, 9), 0), ). 0 -intercept: -intercept: ,, 0) 0,, 0, 0

43 0 Chapter Graphs and Functions. -intercept: 0 -intercept: 0 None 0, 0, ), ) 0, ). 0 -intercept: or, 0), 0) 9 9 -intercepts: 0, 0, 0,, 0 9 0, ). Kestrokes: Y X,T, > GRAPH, 0, 0, 0. Kestrokes: Y ABS X,T, GRAPH 0, 0,, 0. Kestrokes: Y X,T, X,T, GRAPH 9 0, 0,, 0. a) let A 0, 0,000 B,,000 b) c) -intercept 0, 0,000 m,000 0,000 0,000, t 0,000 Value in dollars),000 0,000,000,000,000,000 Time in ears) t The -intercept represents the initial purchase price. 0 t

44 Review Eercises for Chapter 0. m. m is undefined m ,,, 9 There are man solutions to this problem.. 0,,, 7 There are man solutions to this problem ,,, There are man solutions to this problem.. Verbal Model: Proportion: Rise Run Rise Run , feet. 0. L :. L : m, m so the lines are parallel m m L : 0. L : 0. m 0., m 0. m m, m m so the lines are neither. L : 0 L : 0 m m so the lines are perpendicular m m 70. let t, c 990,. and t, c 000,. average rate of change c c $0. t t

45 0 Chapter Graphs and Functions m 0 0. m m a) b) m

46 Review Eercises for Chapter 0 9. m a) b) a) R t t corresponds to 99 b) R 7 $00 c) R $90 9. < 0 a) 0 0 <? 0 b) <? < 0 < 0 < 0 es 0 < 0 no c) ) ) <? 0 d) ) ) <? 0 < 0 < 0 0 < 0 no < 0 es < 0 <

47 0 Chapter Graphs and Functions 0. > 0. > < Kestrokes: Y X,T, 7 0 Y-VARS DRAW, ENTER Kestrokes: X,T, Y 7 0 Y-VARS DRAW, ENTER 0. a) or Note: and cannot be negative. b),, 0,,, Time mowing lawns in hours) 0 0 Time at grocer store in hours). Domain:,, 0,, Range: 0,,. Yes, this relation is a function because each number in the domain is paired to onl one number in the range.. No, this relation is not a function because the in the domain is paired to two numbers and in the range., ), ), ), ) 0, 0)

48 Review Eercises for Chapter h a) h 0 0 b) h c) h h 7 d) ht tt t t or tt g a) b) c) g0 0 g g g d) g. h, if, if > a) h b) h c) h0 0 0 d) h h 9. f 7 0 a) f f f f b) s 0 s 0. Domain: all real values of. s s < < Domain:,,, or < s <, < s <, < s < 0. Verbal Model: Perimeter Length Width Verbal Model: Area Length Width 00 Length Labels: Area A 00 Length 0 Length Function: Length 0 Width A 0 0 < <

49 0 Chapter Graphs and Functions. Domain: < <. Domain: t < or,. Domain: < < Range: < 9 or, 9 Range: 0 < 0, Range: < or, 0 t. Domain: 0 or 0, 0. Domain: < < Range: 0 or 0, Range: < 0, < < or, 0, = + > 0 = 0. f c. f f. f b. Yes, is a function of, because passes the Vertical Line Test. 0. No, is not a function of, because does not pass the Vertical Line Test.. h. h Vertical shift units upward Reflection in the -ais, horizontal shift units to the left, and a vertical shift unit upward.. Horizontal shift unit to the right Reflection in the -ais and a vertical shift unit upward