Identify the asymptotes, domain, and range of

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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