In Exercises 119-122, use transformations of the graph of the greatest imeger ftmdion

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-2 g(x) - f(x) + 1

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-3 g(.t) - jf.x) - 1

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-4 g(x) - f(x + I)

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-5 g(x) - f(x - 1)

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-6 g(x) - J(x - 1) - 2

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-7 g(x) - f(x + 1) + 2

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-8 g(x) - J(- x)

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-9 g(x) - - j(x)

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-10 g(x) - - Jt.x) + 3

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-11 g(x) - f(- x) + 3

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-12 g(x) - !f(x)

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-13 g(x) - 2j(x)

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-14 g(x) - JGx)

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-15 g(x) - f(2t)

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-16 g(x) - - f(i x) +I

In Exercises 1-16,use the graph ofy - j(x) t() graph each function g. .v y-flr) ~ )0. 2) (-17 g(x) - -f(2t) - I

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - f(x) - 1

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - f(x) + I

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - f(x - 1)

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - f(x + I)

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - f(x - 1) + 2

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(.t) - f(x ~ 1) - 2

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - - f(x)

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - f(- x)

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - f(- x) + 1

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - - f(x) + I

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - 2/(.r)

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - ~j(x)

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - f(2t)

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - !(!x)

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x) - 2f(x + 2) + 1

In Exercises 17-32, use the graph of y - f(x) w graph each function g. y (2, 2) y-fl.r) g(x} - 2/(t + 2) - I

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - f(x) + 2

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - !(x) - 2

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - f(x + 2)

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - f(x - 2)

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - - f(x + 2)

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - - f(x - 2)

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - - !f(t + 2)

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - - jf(x - 2)

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - ~J(x + 2) - 2

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(.r) - -Vlx - 2) + 2

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - !!(2x)

In Exercises 33-44. use the graph of y - j(x) t() graph each function g. y - -3 (0, - 2) (4, -2) g(x) - 2/Ux)

In Exercises 45-52, use the graph of y - j(x) t() graph each function g. )' y - f tx) ~ )0,2) , (2, 2) (4,0) ~~~~~~~~7-X g(x) - f(x - 1) - I

In Exercises 45-52, use the graph of y - j(x) t() graph each function g. )' y - f tx) ~ )0,2) , (2, 2) (4,0) ~~~~~~~~7-X g(x) - f(x + I) + 1

In Exercises 45-52, use the graph of y - j(x) t() graph each function g. )' y - f tx) ~ )0,2) , (2, 2) (4,0) ~~~~~~~~7-X g(x) - - f(x - I} + 1

In Exercises 45-52, use the graph of y - j(x) t() graph each function g. )' y - f tx) ~ )0,2) , (2, 2) (4,0) ~~~~~~~~7-X g(x) - - f(x + 1) - I

In Exercises 45-52, use the graph of y - j(x) t() graph each function g. )' y - f tx) ~ )0,2) , (2, 2) (4,0) ~~~~~~~~7-X g(x) - 2/( !x)

In Exercises 45-52, use the graph of y - j(x) t() graph each function g. )' y - f tx) ~ )0,2) , (2, 2) (4,0) ~~~~~~~~7-X g(.r) - l./(2x)

In Exercises 45-52, use the graph of y - j(x) t() graph each function g. )' y - f tx) ~ )0,2) , (2, 2) (4,0) ~~~~~~~~7-X g(x) - }Ax + 1)

In Exercises 45-52, use the graph of y - j(x) t() graph each function g. )' y - f tx) ~ )0,2) , (2, 2) (4,0) ~~~~~~~~7-X g(x} - 2j(x - 1)

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. g(x) - x' - 2

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. g(x) - x1 - 1

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. g(x) - (x - 2)2

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. g(x) - (x - tr

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. h(x) - - (x - 2)2

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. h(x) - - (x - t}'

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. h(x) - (x - 2f + I

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. h(x) - (x - 1) 2 + 2

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. g(x) - 2(x - 2t

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. g(x) - l(x - 1)2

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. h(x) - 2(x - 2)2 - I

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. h(x) - hx - 1)2 - I

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. h(x) - - 2(x + 1)' + I

In Exercises 53-66, begin by graphing the standard quadratic Junction, f(x) - x2. Then use transformations of this graph to graph ilre given function. h(x) - - 2(x + 2)2 + I

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. g(x) - vx + 2

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. g(x) - vx + I

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. g(x) - v7+"2

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. g( ~

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. h(x) - -v7+2

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. h(x) - - Vx+"l

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. h(.r) - V-x + 2

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. h(x) - v::;:+L

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. g(x) - }v7+"2

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. g(x) - 2 Vx+"l

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. h(.r) - v:;-:;:-2 - 2

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. h(x) - I

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. g(x) - 2v7+"2 - 2

In Exercises 67-80, begiiJ. by graphing the square root function, j(x) - VX. Then use transformations of this graph to graph the given function. g(x) - 2Vx+"l - I

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. g(x) - lxl + 4

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. g(x) - lxl + 3

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. g(x) - lx + 41

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. g(x) - lx + 31

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. h(x) - lx + 4J - 2

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. h(x) - Jx + 31 - 2

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. h(x) - - lx + 41

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. h(x) - - lx + 31

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. g(x) - - lx + 41 + I

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. g(.r) - -lx + 41 + 2

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. h(x) - 2lx + 4J

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. h(x) - 2 J.r + 3J

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. g(x) - - 2lx + 41 + I

In Exercises 81-94, begin by graphing the absolute value function, j(x) - lxl. Then use transformations of this graph to graph the given Junction. g(x) - - 2lx + 31 + 2

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. g(x) - x' - 3

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. g(x} - x3 - 2

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. g(x) - (x - 3}

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. g(x) - (x - 2)'

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. h(x) - - .r3

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. h(x) - - (x - 2)

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. h(x) - ;x

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. h(x) - ! x'

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. r(.r) - (x - 3}' + 2

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. r(x) - (x - 2)3 + I

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. h(x) - !(x - 3}' - 2

In Exercises 95-106, begin by graphing 11.-standard cubic function, f(x) - x3. Then use transformations of this graph to graph the given function. h(x) - \(r - 2)3 - I

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. g(x) - ~ + 2

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. g(x} - ~ - 2

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. g(x) ~

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. g(x) ~

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. h(x) - ~

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. h(x) - - ~~

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. r(x) - 2

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. r(x) - t~

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. t(.r) - ~

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. lt(x) - ~

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. g(x) - Y/- x - 2

In Exercises 107-118, begin by graphing the cube roo/ function. j(x) - ~. Then use lramformations of this graph to grttph the given fmu:tion. g(x) - Y/- x + 2

In Exercises 119-122, use transformations of the graph of the greatest imeger ftmdion, f(x) - int(x),/o graph each function. (The graph of j(x) - int(x) is sltownirr Figure 2.23 on page 236.) g(x) - 2 int (x + I)

In Exercises 119-122, use transformations of the graph of the greatest imeger ftmdion, f(x) - int(x),/o graph each function. (The graph of j(x) - int(x) is sltownirr Figure 2.23 on page 236.) g(.r) - 3 int (x - I}

In Exercises 119-122, use transformations of the graph of the greatest imeger ftmdion, f(x) - int(x),/o graph each function. (The graph of j(x) - int(x) is sltownirr Figure 2.23 on page 236.) lt(.r) - int(- x) + 1

In Exercises 119-122, use transformations of the graph of the greatest imeger ftmdion, f(x) - int(x),/o graph each function. (The graph of j(x) - int(x) is sltownirr Figure 2.23 on page 236.) lt(x) - int(- x) - 1

In Exercises 123-126, write a possible equation for the function whose graph is shown. Each graph shows a trausfomwtion of a common function. [-2,S. l]by[- 1, 4, l]

In Exercises 123-126, write a possible equation for the function whose graph is shown. Each graph shows a trausfomwtion of a common function. (-3,3, I] by [-6, 6, I]

In Exercises 123-126, write a possible equation for the function whose graph is shown. Each graph shows a trausfomwtion of a common function. [- 5, 3, l] by(- 5, 10, 1]

In Exercises 123-126, write a possible equation for the function whose graph is shown. Each graph shows a trausfomwtion of a common function. [- 1, 9, 1] by [- 1,), 1]

The function f(x) - 2.9vx + 20.1 models the median height,j(x), in inches, of boys who a re x months of age. The graph off is shown. y 50 40 10 I:........!J:"'---':'~~:---7.:-~:--.Ll::-x o 10 20 m 40 50 ro Age (months) Source: Laura Walther Nathanson. The Portable Pi:diaJriciall for Ptlrml.'i a. Describe how the graph can be obtained using lransfonnationsofthesquareroot f1lnctionf(x) - vx. b. According to the model, what is the median height or boys who are 48 months., or four years. old? Use a calculator and round to the nearest tenth of an inch. llte actual median height for boys at 48 months is 40.8 inches. How well does the model describe the actual height? c. Use the model to find the average rate of change. in inches per month, be tween birth a nd 10 months. Round to the nearest tenth. d. Usc the model to find the average rate o f change. in inches pe r month, between 50 and 60 months.. Round to the nearest tenth. How does this compare \\~th your answer in part (c)? How is this difference shown by the graph?

The function J{x) - 3.1 VX + 19 models the median height, f(x), in inches, of girls whoarex months of age. The graph of / is shown. 50 40 10 Girls' Heights Age (months) Source: Laura Walther Nathanson, The Portable Peditltridan for Ptm:Jils a. Describe how the graph can be obtained using transformations of the square root function f(x) - '\IX. b. According to the model, what is the median height of girls who are 48 months, or 4 years. old? Use a calculator and round to the nearest tenth of an inch. The actual median height for girls at 48 months is 40.2 inches. How well does the model describe the actual height? c. Use the model to find the average rate o f change. in inches per mont h, be tween birth and tO months. Round to the nearest tenth. d. Use the model to find the average rate o f change. in inches pe r month, between 50 and 60 months. Round to the nearest te nth. How does this compare with your answer in part (c)? How is this diffe rence shown by the graph?

What must be done to a function's equation so that its graph is shifted vertically upward?

What must be done to a function's equation so that its graph is shifted horizontally to the right?

What must be done to a function's equation so that its graph is reflected about the x-axis?

What must be done to a function's equation so that its graph is reflected about the y-axis?

What must be done to a function's equation so that its graph is stretched vertically.

What must be done to a function's equation so that its graph is shrunk horizontally.

a. Use a graphing utility to graphf(x) - x1 + 1. b. Graph f(x) - x2 + 1,g(x) - f(2x),h(x) - f(3x), a nd k(x) - f(4x ) in the same viewing rectangle. c. Describe the relationship among the graphs of f, g. h, and k, with emphasis on different values of x for points on all four gra phs that give the same y-coordinate. d. Generalize by describing the relationship between the graph off and the graph o f g, where g(x) - fl. ex) for c > 1. e .. Try o ut your generalization by sketching the gra phs of f(cx) for c - 1, c - 2, c - 3, and c - 4 for a function o f your choice.

a. Usc a graphing utility to graph f(x) - x' + 1. b. Graphf(.r) - x2 + l. g(x) - f(lx),and h (x) - f(!x) in the same viewing rectangle. c. Describe the relationship among the graphs off g, a nd h. with emphasis on diffe rent values of x for points on all three graphs that give the same y-coordinate. d. Generalize by describing the relationship between the graph off and the graph o f g, where g(x} - f(cx) for O< c < l. e. Try out your generalization by sketching the graphs or !(ex) for c - 1, and c - !. and c - ! for a function of your choice.

During the winter, you program your home thermostat so that at midnight, thf! temperature is 55. 1J1is temperalltre is maitllained uflli/6 A .. lf. Then the house begins to wann up so that by 9 A.M. the temperature is 65. At6 P.M. the house begins to cool. By 9 P.M., the temperature is again 55. The graph ilfustrates home temperature, f(t), as a function of hours after midnight, 1. .. 7()> 65 6()> s~ 50' 0 3 Home Temperature as a Function of Time y - f [t) 6 9 12 IS 18 21 24 Hours after Midnight In Exercises J 37-140, determine whether each stateme/11 makes sense or does not make sense, and explain your reasoning. If the statement makes sense, graph the new function on the domain (0, 24]. If the statement does not make sense, correct the ftmcti.on in the statement and graph the corrected ftmction on the domain (0,24]. I decided to keep the house 5c warmer than before, so [ reprogrammed the thermostat toy - f(t) + 5.

During the winter, you program your home thermostat so that at midnight, thf! temperature is 55. 1J1is temperalltre is maitllained uflli/6 A .. lf. Then the house begins to wann up so that by 9 A.M. the temperature is 65. At6 P.M. the house begins to cool. By 9 P.M., the temperature is again 55. The graph ilfustrates home temperature, f(t), as a function of hours after midnight, 1. .. 7()> 65 6()> s~ 50' 0 3 Home Temperature as a Function of Time y - f [t) 6 9 12 IS 18 21 24 Hours after Midnight In Exercises J 37-140, determine whether each stateme/11 makes sense or does not make sense, and explain your reasoning. If the statement makes sense, graph the new function on the domain (0, 24]. If the statement does not make sense, correct the ftmcti.on in the statement and graph the corrected ftmction on the domain (0,24]. I decided to keep the house 5 cooler tha n be fore, so I reprogrammed the thermostat toy - f(t) - 5.

During the winter, you program your home thermostat so that at midnight, thf! temperature is 55. 1J1is temperalltre is maitllained uflli/6 A .. lf. Then the house begins to wann up so that by 9 A.M. the temperature is 65. At6 P.M. the house begins to cool. By 9 P.M., the temperature is again 55. The graph ilfustrates home temperature, f(t), as a function of hours after midnight, 1. .. 7()> 65 6()> s~ 50' 0 3 Home Temperature as a Function of Time y - f [t) 6 9 12 IS 18 21 24 Hours after Midnight In Exercises J 37-140, determine whether each stateme/11 makes sense or does not make sense, and explain your reasoning. If the statement makes sense, graph the new function on the domain (0, 24]. If the statement does not make sense, correct the ftmcti.on in the statement and graph the corrected ftmction on the domain (0,24]. I decided to change the heating schedule to start one hour earlier than before, so I reprogrammed the thermosta t to y - f(t - 1).

During the winter, you program your home thermostat so that at midnight, thf! temperature is 55. 1J1is temperalltre is maitllained uflli/6 A .. lf. Then the house begins to wann up so that by 9 A.M. the temperature is 65. At6 P.M. the house begins to cool. By 9 P.M., the temperature is again 55. The graph ilfustrates home temperature, f(t), as a function of hours after midnight, 1. .. 7()> 65 6()> s~ 50' 0 3 Home Temperature as a Function of Time y - f [t) 6 9 12 IS 18 21 24 Hours after Midnight In Exercises J 37-140, determine whether each stateme/11 makes sense or does not make sense, and explain your reasoning. If the statement makes sense, graph the new function on the domain (0, 24]. If the statement does not make sense, correct the ftmcti.on in the statement and graph the corrected ftmction on the domain (0,24]. I decided to change the heating schedule to start one hour later than be fore. so I reprogrammed the thermostat to }' - f(t + 1).

In Exercises 141-144, determine whether each statement is lnte or false. If the statemellt is false, make the necessmy clrange(s) to produce a tme slatenumt. If f(x) - !x! and g(x) - Jx + 3) + 3. then the gra ph of g is a translation of the graph off three units to the right and three units upward.

In Exercises 141-144, determine whether each statement is lnte or false. If the statemellt is false, make the necessmy clrange(s) to produce a tme slatenumt. If f(x) - -vx and g(x) - V::X, then f and g have identical graphs.

In Exercises 141-144, determine whether each statement is lnte or false. If the statemellt is false, make the necessmy clrange(s) to produce a tme slatenumt. If f(x) - x 2 and g(x) - 5(x1 - 2), then the graph of g can be obtained fTom the grnph of f by stretching f five units followed by a downward shift of two units.

In Exercises 141-144, determine whether each statement is lnte or false. If the statemellt is false, make the necessmy clrange(s) to produce a tme slatenumt. If f(x) - x> and g(x) - - (x - 3)' - 4, then the grnph of g can be obtained from the graph off by mo\ingf three units to the right. reflecting a bout the x-axis, and then moving the resulting graph down four units.

In Exercises 145-148, functions f and g are graphed in the saml! rectangular coorditwte system. If g is obtained from f through a sequence o.ftransfornwlionJ~find an equation for g. .l'

In Exercises 145-148, functions f and g are graphed in the saml! rectangular coorditwte system. If g is obtained from f through a sequence o.ftransfornwlionJ~find an equation for g. y

In Exercises 145-148, functions f and g are graphed in the saml! rectangular coorditwte system. If g is obtained from f through a sequence o.ftransfornwlionJ~find an equation for g. y 5 4 -3 -4 -5 flx) - Vx

In Exercises 145-148, functions f and g are graphed in the saml! rectangular coorditwte system. If g is obtained from f through a sequence o.ftransfornwlionJ~find an equation for g. y 5 f!.<J - '\Ii6=Xf -3 -4 -5

For Exercises 149-152, asstmu! that (a. b) is a poilll on the graph of f. What is the corresponding point 011 the graph of each of the following functions? y - f(- x)

For Exercises 149-152, asstmu! that (a. b) is a poilll on the graph of f. What is the corresponding point 011 the graph of each of the following functions? y - 2f(x)

For Exercises 149-152, asstmu! that (a. b) is a poilll on the graph of f. What is the corresponding point 011 the graph of each of the following functions? y - f(x - 3)

For Exercises 149-152, asstmu! that (a. b) is a poilll on the graph of f. What is the corresponding point 011 the graph of each of the following functions? y - f(x) - 3

Exercises 153-155 will help you prepare for the material covered in the next section. In rercises 153-154, perform the indicated operation or operations. (2x - l)(x2 ~ x - 2)

Exercises 153-155 will help you prepare for the material covered in the next section. In rercises 153-154, perform the indicated operation or operations. (f(x)) 2 - 2f(x) + 6. where f(x) - 3x - 4

Exercises 153-155 will help you prepare for the material covered in the next section. In rercises 153-154, perform the indicated operation or operations. implify: 2 3 . - - 1