Answer:
Match list below
Step-by-step explanation:
The Sine Function
The general expression for the sine function is
[tex]f(x)=A.sin(w.x+z)+M[/tex]
Where:
A=Amplitude
w=angular frequency
x = variable
z = phase shift
M = Midline or vertical shift
The angular frequency can be expressed as a function of the period T
[tex]\displaystyle w=\frac{2\pi}{T}[/tex]
Solving for T
[tex]\displaystyle T=\frac{2\pi}{w}[/tex]
Now, let's analyze each description and find its sine function
Amplitude: 2
The only function that has amplitude 2 (the coefficient of the sine) is
g(x) = 2sin(8x + pi) +1
Period: 1/8
Let's compute w
[tex]\displaystyle w=\frac{2\pi}{\frac{1}{8} }=16\pi[/tex]
We find no function with such an angular frequency
Midline: y = 1
There is only one function with M=1 as compared to the general function
g(x) = 2sin(8x + pi) +1
Amplitude: 4
We find two functions:
f(x) = 4sin((1/pi)x -2) +8
q(x) = 4sin(2x - pi) + 8
Period: 1/2
[tex]\displaystyle w=\frac{2\pi}{\frac{1}{2} }=4\pi[/tex]
No function can be found with that value of w
Midline: y = 8
Two functions have such a midline
f(x) = 4sin((1/pi)x -2) +8
q(x) = 4sin(2x - pi) + 8
Amplitude: 8
We can find two functions like that
p(x) = 8sin(pi x +4) +2
h(x) = 8sin(pi x - 2) + 4
Period: 1/pi
[tex]\displaystyle w=\frac{2\pi}{\frac{1}{\pi} }=2\pi^2[/tex]
No function complies with that condition
Midline: y = 4
h(x) = 8sin(pi x - 2) + 4
is the only one to have midline y=4
Amplitude: 1
r(x) = sin(4x +8) +2
Midline: y = 2
p(x) = 8sin(pi x +4) +2
r(x) = sin(4x +8) +2
Answer:
amplitude:8
period:2
midline:4
h(x)=8sin(pix-2)+4
amplitude:4
period: pi
midline:8
q(x)=4sin(2x-pi)+8
amplitude:1
period:pi/2
midline:2
r(x)sin(4x+8)+2
amplitude:2
period:pi/4
midline:1
g(x)=2sin(8x+x)+1
Step-by-step explanation:
PLATO/Edmentum
