Part II: The Answers
178
Answers
101–200
149.
f
(x) = 2 sin(2x)
For the function f x
A
B x C
B
D
( )
sin
=
−
( )
+ , the amplitude is A , the period is
2π
B
, the phase shift is C
B
, and the midline is y = D. The function has a period of π, so
one possible value of B is B = 2. If you use a sine function to describe the graph, there’s
no phase shift, so you can use C = 0. The line y = 0 is the midline of the function so that
D = 0. Last, the amplitude is 2, so you can use A = 2 because the function increases for
values of x that are slightly larger than zero. Therefore, the function f x
x
( )
sin( )
= 2
2
describes the given graph. Note that you can also use other functions to describe
this graph.
150.
f
(x) = 2 cos(2x)
For the function f x
A
B x C
B
D
( )
cos
=
−
( )
+ , the amplitude is A , the period is 2π
B
,
the phase shift is C
B
, and the midline is y = D. The function has a period of π, so one possible value of B is B = 2. If you use a cosine function to describe the graph, there’s no phase
shift; therefore, you can use C = 0. The line y = 0 is the midline of the function, so D = 0.
Last, the amplitude is 2; you can use A = 2 because the function decreases for values of x
that are slightly larger than zero. Therefore, the function f
(x) = 2 cos(2x) describes the
given graph. Note that you can also use other functions to describe this graph.
151.
f x
x
( )
cos
= −
( )
2
1
2
For the function f x
A
B x C
B
D
( )
cos
=
−
( )
+ , the amplitude is A , the period is 2π
B
, the
phase shift is C
B
, and the midline is y = D. The function has a period of 4π, so one possible
value of B is B = 1
2
. If you use a cosine function to describe the graph, there’s no phase
shift, so you can use C = 0. The line y = 0 is the midline of the function, so D = 0. Last, the
amplitude is 2, so you can use A = –2 because the function increases for values of x that
are slightly larger than zero. Therefore, the function f x
x
( )
cos
= −
( )
2
1
2
describes the
given graph. Note that you can also use other functions to describe this graph.
152.
f
(x) = 2 cos(2x) + 1
For the function f x
A
B x C
B
D
( )
cos
=
−
( )
+ , the amplitude is A , the period is 2π
B
, the
phase shift is C
B
, and the midline is y = D. The function has a period of π, so one possible
value of B is B = 2. If you use a cosine function to describe the graph, there’s no phase
shift, so you can use C = 0. The line y = 1 is the midline of the function, so D = 1. Last, the
amplitude is 2, so you can use A = 2 because the function decreases for values of x that
are slightly larger than zero. Therefore, the function f
(x) = 2 cos(2x) + 1 describes the
given graph. Note that you can also use other functions to describe this graph.
178
Answers
101–200
149.
f
(x) = 2 sin(2x)
For the function f x
A
B x C
B
D
( )
sin
=
−
( )
+ , the amplitude is A , the period is
2π
B
, the phase shift is C
B
, and the midline is y = D. The function has a period of π, so
one possible value of B is B = 2. If you use a sine function to describe the graph, there’s
no phase shift, so you can use C = 0. The line y = 0 is the midline of the function so that
D = 0. Last, the amplitude is 2, so you can use A = 2 because the function increases for
values of x that are slightly larger than zero. Therefore, the function f x
x
( )
sin( )
= 2
2
describes the given graph. Note that you can also use other functions to describe
this graph.
150.
f
(x) = 2 cos(2x)
For the function f x
A
B x C
B
D
( )
cos
=
−
( )
+ , the amplitude is A , the period is 2π
B
,
the phase shift is C
B
, and the midline is y = D. The function has a period of π, so one possible value of B is B = 2. If you use a cosine function to describe the graph, there’s no phase
shift; therefore, you can use C = 0. The line y = 0 is the midline of the function, so D = 0.
Last, the amplitude is 2; you can use A = 2 because the function decreases for values of x
that are slightly larger than zero. Therefore, the function f
(x) = 2 cos(2x) describes the
given graph. Note that you can also use other functions to describe this graph.
151.
f x
x
( )
cos
= −
( )
2
1
2
For the function f x
A
B x C
B
D
( )
cos
=
−
( )
+ , the amplitude is A , the period is 2π
B
, the
phase shift is C
B
, and the midline is y = D. The function has a period of 4π, so one possible
value of B is B = 1
2
. If you use a cosine function to describe the graph, there’s no phase
shift, so you can use C = 0. The line y = 0 is the midline of the function, so D = 0. Last, the
amplitude is 2, so you can use A = –2 because the function increases for values of x that
are slightly larger than zero. Therefore, the function f x
x
( )
cos
= −
( )
2
1
2
describes the
given graph. Note that you can also use other functions to describe this graph.
152.
f
(x) = 2 cos(2x) + 1
For the function f x
A
B x C
B
D
( )
cos
=
−
( )
+ , the amplitude is A , the period is 2π
B
, the
phase shift is C
B
, and the midline is y = D. The function has a period of π, so one possible
value of B is B = 2. If you use a cosine function to describe the graph, there’s no phase
shift, so you can use C = 0. The line y = 1 is the midline of the function, so D = 1. Last, the
amplitude is 2, so you can use A = 2 because the function decreases for values of x that
are slightly larger than zero. Therefore, the function f
(x) = 2 cos(2x) + 1 describes the
given graph. Note that you can also use other functions to describe this graph.