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 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.
Identify the asymptotes, domain, and range of
each function.
3. ANSWER: 7. ANSWER: x = –4, f (x) = 0; D = {x | x
0}
–4}; R = {f (x) | f (x)
5. ANSWER: 9. ANSWER: x = –6, f (x) = –2; D = {x | x
–2}
–6}; R = {f (x) | f (x)
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Graph each function. State the domain and
range.
Page 1
ANSWER: x = –6, f (x) = –2; D = {x | x –6}; R = {f (x) | f (x)
–2}
8-3 Graphing
Reciprocal Functions
D = {x | x
6}; R = {f (x) | f (x)
0}
Graph each function. State the domain and
range.
15. 11. ANSWER: ANSWER: D = {x | x
0}; R = {f (x) | f (x)
3}
D = {x | x
0}; R = {f (x) | f (x)
0}
17. ANSWER: 13. ANSWER: D = {x | x
5}; R = {f (x) | f (x)
0}
D = {x | x
6}; R = {f (x) | f (x)
0}
19. ANSWER: 15. ANSWER: D = {x | x
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D = {x | x
0}; R = {f (x) | f (x)
3}
–3}; R = {f (x) | f (x)
6}
Page 2
D = {x | x Reciprocal
(x) | f (x) 0}
5}; R = {fFunctions
8-3 Graphing
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.
19. 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.
ANSWER: 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?
D = {x | x
–3}; R = {f (x) | f (x)
ANSWER: 6}
a.
21. b.
ANSWER: c. 13.7 mi
D = {x | x
–4}; R = {f (x) | f (x)
–2}
Graph each function. State the domain and
range.
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.
25. ANSWER: 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: eSolutions
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a.
D = {x | x
2}; R = {f (x) | f (x)
0}
Page 3
D=
c. 13.7 mi Reciprocal Functions
8-3 Graphing
R = {f (x) | f (x)
0}
Graph each function. State the domain and
range.
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.
25. ANSWER: b. Graph the function.
c. If a two-seam fastball reaches the plate in 0.48
second, what was its speed?
ANSWER: a.
D = {x | x
2}; R = {f (x) | f (x)
0}
b.
27. ANSWER: c. 126 ft/s
Graph each function. State the domain and
range, and identify the asymptotes.
D=
31. R = {f (x) | f (x)
0}
29. BASEBALL The distance from the pitcher’s mound
to home plate is 60.5 feet.
ANSWER: D = {x | x –2}; R = {f (x) | f (x)
(x) = –5
–5}; x = –2, f
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.
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c. IfManual
a two-seam
fastball
reaches
second, what was its speed?
the plate in 0.48
Page 4
c. 126 ft/s Reciprocal Functions
8-3 Graphing
Graph each function. State the domain and
range, and identify the asymptotes.
35. ANSWER: D = {x | x 7}; R = {f (x) | f (x)
–8
31. ANSWER: D = {x | x –2}; R = {f (x) | f (x)
(x) = –5
–8}; x = 7, f (x) =
–5}; x = –2, f
37. MULTIPLE REPRESENTATIONS Consider the
functions
and
33. a. TABULAR Make a table of values comparing
the two functions.
ANSWER: D = {x | x 4}; R = {f (x) | f (x)
3
3}; x = 4, f (x) =
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.
35. 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.
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 positive portion of
graph of
is similar to the Positive values of x produce
positive values of f (x). The negative portion of
appears to be a reflection of
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.
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.
a.
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41. CHALLENGE Write two different reciprocal Page 6
functions with graphs having the same vertical and
horizontal asymptotes. Then graph the functions.
ANSWER: B
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.
47. If –1 < a < b < 0, then which of the following has the
greatest value?
Aa–b
ANSWER: Bb–a
and Sample answer:
Ca+b
D 2b – a
ANSWER: B
Simplifying each expression.
49. 43. SHORT RESPONSE What is the value of (x + y)
2
2
(x + y) if xy = –3 and x + y = 10?
ANSWER: –2p
ANSWER: 4
45. If
and d > 1, then c could equal ___.
51. A
ANSWER: B
C
Graph each function. State the domain and
range.
x
D
53. y = 5(2)
ANSWER: D = {x | x is all real numbers}, R = {y | y > 0}
ANSWER: B
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< a <- bPowered
< 0, then
which
47. If –1Manual
greatest value?
of the following has the
Page 7
ANSWER: 8-3 Graphing Reciprocal Functions
Graph each function. State the domain and
range.
Find (f + g)(x), (f - g)(x), (f · g)(x), and
for each f (x) and g(x).
x
53. y = 5(2)
ANSWER: D = {x | x is all real numbers}, R = {y | y > 0}
57. ANSWER: 55. ANSWER: D = {x | x is all real numbers}, R = {y | y > 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.
ANSWER: Find (f + g)(x), (f - g)(x), (f · g)(x), and
for each f (x) and g(x).
Graph each polynomial function. Estimate the xcoordinates at which the relative maxima and
relative minima occur. State the domain and
range for each function.
57. 4
2
61. f (x) = x – 8x + 10
ANSWER: ANSWER: eSolutions Manual - Powered by Cognero
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ANSWER: 8-3 Graphing Reciprocal Functions
Graph each polynomial function. Estimate the xcoordinates at which the relative maxima and
relative minima occur. State the domain and
range for each function.
4
2
61. f (x) = x – 8x + 10
ANSWER: Sample answer = rel. max. at x = 0, rel. min. at x = –
2 and at x = 2; D = {all real numbers}, R = {f (x) | f
(x) –6}
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