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glamrockqueen7 2021-10-14 Answered

Consider the function \(\displaystyle{f{{\left({x}\right)}}}={2}{\sin{{\left(\pi{2}{\left({x}−{3}\right)}\right)}}}+{4}\).
State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values.
Hints for the maximum and minimum values of f(x):
The maximum value of \(\displaystyle{y}={\sin{{\left({x}\right)}}}\) is \(\displaystyle{y}={1}\) and the corresponding x values are \(\displaystyle{x}=\pi{2}\) and multiples of \(\displaystyle{2}\pi\) less than and more than this x value. You may want to solve \(\displaystyle\pi{2}{\left({x}−{3}\right)}=\pi{2}\).
The minimum value of \(\displaystyle{y}={\sin{{\left({x}\right)}}}\) is \(\displaystyle{y}=−{1}\) and the corresponding x values are \(\displaystyle{x}={3}\pi{2}\) and multiples of \(\displaystyle{2}\pi\) less than and more than this x value. You may want to solve \(\displaystyle\pi{2}{\left({x}−{3}\right)}={3}\pi{2}\).
If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles.
If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.
For x in the interval [0, P], the maximum y-value and corresponding x-value is at:
\(\displaystyle{x}=\)
\(\displaystyle{y}=\)
For x in the interval [0, P], the minimum y-value and corresponding x-value is at:
\(\displaystyle{x}=\)
\(\displaystyle{y}=\)

nagasenaz 2021-10-11 Answered

Consider the function \(\displaystyle{f{{\left({x}\right)}}}={3}{\sin{{\left({\frac{{\pi}}{{{3}}}}{\left({x}−{4}\right)}\right)}}}+{5}\).
State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values.
Enter the exact answers.
Amplitude: \(\displaystyle{A}=\)
Period: \(\displaystyle{P}=\)
Midline: \(\displaystyle{y}=\)
The phase shift is:
a. up 4 units
b. 4 units to the right
c. 4 units to the left
d. 5 units to the left
The vertical translation is:
a. up 4 units
b. down 5 units
c. up 5 units
d. down 4 units
Hints for the maximum and minimum values of f(x):
The maximum value of \(\displaystyle{y}={\sin{{\left({x}\right)}}}\) is \(\displaystyle{y}={1}\) and the corresponding x values are \(\displaystyle{x}={\frac{{\pi}}{{{2}}}}\) and multiples of \(\displaystyle{2}\pi\) less than and more than this x value. You may want to solve \(\displaystyle{\frac{{\pi}}{{{3}}}}{\left({x}−{4}\right)}={\frac{{\pi}}{{{2}}}}\).
The minimum value of \(\displaystyle{y}={\sin{{\left({x}\right)}}}\) is \(\displaystyle{y}=−{1}\) and the corresponding x values are \(\displaystyle{x}={\frac{{{3}\pi}}{{{2}}}}\) and multiples of \(\displaystyle{2}\pi\) less than and more than this x value. You may want to solve \(\displaystyle{\frac{{\pi}}{{{3}}}}{\left({x}−{4}\right)}={\frac{{{3}\pi}}{{{2}}}}\).
If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles.
If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.
For x in the interval [0, P], the maximum y-value and corresponding x-value is at:
x=
y=
For x in the interval [0, P], the minimum y-value and corresponding x-value is at:
\(\displaystyle{x}=\)
\(\displaystyle{y}=\)

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