Identify the asymptotes, domain, and range of

[Pages:9]8-3 Graphing Reciprocal Functions

Identify the asymptotes, domain, and range of each function.

5. ANSWER:

1.

ANSWER: x = 1,f (x) = 0; D = {x | x

0}

1} R = {f (x) | f (x)

Graph each function. State the domain and range.

3.

ANSWER:

Identify the asymptotes, domain, and range of each function.

7.

ANSWER: x = ?4,f (x) = 0; D = {x | x

0}

?4}; R = {f (x) | f (x)

5. ANSWER:

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9.

ANSWER: x = ?6,f (x) = ?2; D = {x | x

?2}

?6}; R = {f (x) | f (x)

Graph each function. State the domain and Page 1 range.

ANSWER: x = ?6,f (x) = ?2; D = {x | x ?6}; R = {f (x) | f (x) 8-3 Gra?p2h}ing Reciprocal Functions

Graph each function. State the domain and range.

11.

ANSWER:

D = {x | x 6} R = {f (x) | f (x) 0} 15.

ANSWER:

D = {x | x 0} R = {f (x) | f (x) 0} 13.

ANSWER:

D = {x | x 6} R = {f (x) | f (x) 0} 15.

ANSWER:

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D = {x | x 0} R = {f (x) | f (x) 3}

D = {x | x 0} R = {f (x) | f (x) 3} 17.

ANSWER:

D = {x | x 5} R = {f (x) | f (x) 0} 19.

ANSWER:

D = {x | x ?3}; R = {f (x) | f (x) 6}

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8-3 GDr=ap{hxin| gx Re5ci}prRoc=al{fF(ux)n|cft(ioxn) s 0} 19.

ANSWER:

D = {x | x ?3}; R = {f (x) | f (x) 6} 21.

ANSWER:

D = {x | x ?4}; R = {f (x) | f (x) ?2}

23. CYCLING Marina's New Year's resolution is to ride her bike 5000 miles.

a. If m represents the mileage Marina rides each day and d represents the number of days, write an equation to represent the mileage each day as a function of the number of days that she rides.

b. Graph the function.

c. If she rides her bike every day of the year, how many miles should she ride each day to meet her goal?

ANSWER: a.

b.

D = {x | x ?4}; R = {f (x) | f (x) ?2}

23. CYCLING Marina's New Year's resolution is to ride her bike 5000 miles.

a. If m represents the mileage Marina rides each day and d represents the number of days, write an equation to represent the mileage each day as a function of the number of days that she rides.

b. Graph the function.

c. If she rides her bike every day of the year, how many miles should she ride each day to meet her goal?

eSolutAioNnsSMWanEuaRl -:Powered by Cognero a.

c. 13.7 mi Graph each function. State the domain and range. 25.

ANSWER:

D = {x | x 2} R = {f (x) | f (x) 0}

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8-3 Gc.ra13p.h7imngi Reciprocal Functions Graph each function. State the domain and range.

25. ANSWER:

D = {x | x 2} R = {f (x) | f (x) 0}

D =

R = {f (x) | f (x) 0}

29. BASEBALL The distance from the pitcher's mound to home plate is 60.5 feet.

a. If r represents the speed of the pitch and t represents the time it takes the ball to get to the plate, write an equation to represent the speed as a function of time.

b. Graph the function.

c. If a two-seam fastball reaches the plate in 0.48 second, what was its speed?

ANSWER: a.

b.

27. ANSWER:

c. 126 ft/s

Graph each function. State the domain and range, and identify the asymptotes.

D =

R = {f (x) | f (x) 0}

29. BASEBALL The distance from the pitcher's mound to home plate is 60.5 feet.

a. If r represents the speed of the pitch and t represents the time it takes the ball to get to the plate, write an equation to represent the speed as a function of time.

b. Graph the function.

eSolutcio.nIsfMaatnwuaol -sPeoawmerefdasbtybCaollgnrearoches the plate in 0.48 second, what was its speed?

31.

ANSWER:

D = {x | x ?2}; R = {f (x) | f (x) (x) = ?5

?5}; x = ?2,f

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8-3 Gc.ra1p26hifnt/gs Reciprocal Functions

Graph each function. State the domain and range, and identify the asymptotes.

31.

ANSWER:

D = {x | x ?2}; R = {f (x) | f (x) (x) = ?5

?5}; x = ?2,f

35.

ANSWER:

D = {x | x 7} R = {f (x) | f (x) ?8

?8}; x = 7,f (x) =

33.

ANSWER:

D = {x | x 4} R = {f (x) | f (x) 3

3} x = 4,f (x) =

35.

37. MULTIPLE REPRESENTATIONS Consider the

functions

and

a. TABULAR Make a table of values comparing the two functions.

b. GRAPHICAL Use the table of values to graph both functions.

c. VERBAL Compare and contrast the two graphs.

d. ANALYTICAL Make a conjecture about the difference between the graphs of functions of the

form

with an even exponent in the

denominator and those with an odd exponent in the denominator.

ANSWER: a.

ANSWER:

D = {x | x 7} R = {f (x) | f (x) ?8

?8}; x = 7,f (x) =

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denominator and those with an odd exponent in the denominator.

8-3 Graphing Reciprocal Functions ANSWER: a.

d. Sample answer: When n is even, the graph will show symmetry with respect to the y -axis. When the n is odd, the graph will show symmetry with respect to the origin.

39. REASONING Compare and contrast the graphs of each pair of equations.

a.

b.

c.

d. Without making a table of values, use what you observed in parts a-c to sketch a graph of

b.

c. The positive portion of

is similar to the

graph of

Positive values of x produce

positive values of f (x). The negative portion of

appears to be a reflection of

over the x-axis. Negative values of x

produce positive values of g(x).

d. Sample answer: When n is even, the graph will show symmetry with respect to the y -axis. When the n is odd, the graph will show symmetry with respect to the origin.

39. REASONING Compare and contrast the graphs of each pair of equations.

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ANSWER: a. The first graph has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. The second graph is translated 7 units up and has a vertical asymptote at x = 0 and a horizontal asymptote at y = 7. b. Both graphs have a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. The second graph is stretched by a factor of 4. c. The first graph has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. The second graph is translated 5 units to the left and has a vertical asymptote at x = ?5 and a horizontal asymptote at y = 0. d.

41. CHALLENGE Write two different reciprocal Page 6 functions with graphs having the same vertical and horizontal asymptotes. Then graph the functions.

8-3 Graphing Reciprocal Functions

41. CHALLENGE Write two different reciprocal functions with graphs having the same vertical and horizontal asymptotes. Then graph the functions.

ANSWER:

Sample answer:

and

ANSWER: B

47. If ?1 < a < b < 0, then which of the following has the greatest value? A a ? b B b ? a C a + b D 2b ? a

ANSWER: B

Simplifying each expression.

43. SHORT RESPONSE What is the value of (x + y) (x + y ) if xy = ?3 and x2 + y 2 = 10?

ANSWER: 4

49.

ANSWER: ?2p

45. If

and d > 1, then c could equal ___.

51.

A ANSWER:

B

C

D

ANSWER: B

eS4o7l.utIiofn?s1M 0}

59. GEOMETRY The width of a rectangular prism is w centimeters. The height is 2 centimeters less than the width. The length is 4 centimeters more than the width. If the volume of the prism is 8 times the measure of the length, find the dimensions of the prism.

Find (f + g)(x), (f - g)(x), (f ? g)(x), and for eachf (x) and g(x).

57. ANSWER:

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ANSWER:

Graph each polynomial function. Estimate the xcoordinates at which the relative maxima and relative minima occur. State the domain and range for each function. 61. f (x) = x4 ? 8x2 + 10 ANSWER:

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