Answer:
<em>Match list below</em>
Step-by-step explanation:
<u>The Sine Function</u>
The general expression for the sine function is
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
Solving for T
Now, let's analyze each description and find its sine function
<u>Amplitude: 2</u>
The only function that has amplitude 2 (the coefficient of the sine) is
g(x) = 2sin(8x + pi) +1
<u>Period: 1/8</u>
Let's compute w
We find no function with such an angular frequency
<u>Midline: y = 1</u>
There is only one function with M=1 as compared to the general function
g(x) = 2sin(8x + pi) +1
<u>Amplitude: 4</u>
We find two functions:
f(x) = 4sin((1/pi)x -2) +8
q(x) = 4sin(2x - pi) + 8
<u>Period: 1/2</u>
No function can be found with that value of w
<u>Midline: y = 8
</u>
Two functions have such a midline
f(x) = 4sin((1/pi)x -2) +8
q(x) = 4sin(2x - pi) + 8
<u>Amplitude: 8</u>
We can find two functions like that
p(x) = 8sin(pi x +4) +2
h(x) = 8sin(pi x - 2) + 4
<u>Period: 1/pi</u>
No function complies with that condition
<u>Midline: y = 4</u>
h(x) = 8sin(pi x - 2) + 4
is the only one to have midline y=4
<u>Amplitude: 1</u>
r(x) = sin(4x +8) +2
<u>Midline: y = 2</u>
p(x) = 8sin(pi x +4) +2
r(x) = sin(4x +8) +2