For the functions y = A tan B x − C and y = A cot B x − C with B > 0 , the vertical scaling factor is _____ , the period is _____ , and the phase shift is _____ .
For the functions y = A tan B x − C and y = A cot B x − C with B > 0 , the vertical scaling factor is _____ , the period is _____ , and the phase shift is _____ .
Solution Summary: The author explains the properties of the functions, y=Amathrmtan(Bx-C), with B>0.
For the functions
y
=
A
tan
B
x
−
C
and
y
=
A
cot
B
x
−
C
with
B
>
0
, the vertical scaling factor is
_____
, the period is
_____
, and the phase shift is
_____
.
Find the horizontal shift of the function defined by the following equation,
(2)
2 4 cos 2x
Choose the correct answer:
OA. Horizontal shift
3.
Horizontal shift
OB.
6.
7T
OC. Horizontal shift
6.
7T
Horizontal shift
OD.
3.
Reset Selection
Consider the following function.
y = -3.5 cosx + 4)
(a) Using pencil and paper, not a graphing utility, determine the amplitude, period, and phase shift for the function.
amplitude
period
phase shift
(b) Use a graphing utility to graph the function for two complete cycles. [In choosing an appropriate viewing rectangle, you
will need to use the information obtained in part (a).]
y
y
4
4|
2.
-12
\12 я - 12
12 л - 6
-2
2
-4
y
y
4
4-
2
2
-3
12 л - 3
12 л - 9
-2
(c) Use the graphing utility to estimate the coordinates of the highest points on the graph. (Round your answers to two
decimal places.)
(x, y) =
(smaller x-value)
(x, y) = (|
(larger x-value)
Use the graphing utility to estimate the coordinates of the lowest points on the graph. (Round your answers to two decimal
1.
-5TT/4
-8
-7-
6
5
WW
-2
-3/4
-TT/2
-TT/4
0
-1-
TT/4
Give the midline (vertical shift) of the function.
d. Give the amplitude of the function.
Amplitude = 3
TT/2
+
a.
On the graph shown, highlight one period of the function.
b.
Give the period of this function.
3TT/4
e. Find an equation for this graph of the form f(x)= a sin(b(x−c))+d
(Bonus points if you can give more than one answer!)
3sin(
f. Find an equation for this graph of the form f(x) = a cos(b(x-c))+d
577/4
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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