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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)
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.
0}; R = {f (x) | f (x)
3}
D = {x | x
0}; R = {f (x) | f (x)
0}
5}; R = {f (x) | f (x)
0}
D = {x | x
6}; R = {f (x) | f (x)
0}
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.
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)
a.
21. b.
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?
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?
D = {x | x
2}; R = {f (x) | f (x)
0}
b.
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.
eSolutions
- Powered
by Cognero
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.
35. ANSWER: D = {x | x 7}; R = {f (x) | f (x)
–8
–8}; x = 7, f (x) =
Page 5
denominator and those with an odd exponent in the
denominator.
8-3 Graphing Reciprocal Functions
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.
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.
47. If –1 < a < b < 0, then which of the following has the
greatest value?
Aa–b
Ca+b
D 2b – a
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?
45. If
and d > 1, then c could equal ___.
51. A
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}
eSolutions
by Cognero
< a <- bPowered
< 0, then
which
47. If –1Manual
greatest value?
of the following has the
Page 7
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
Page 8
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}