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Question 1 of 5Find the period, amplitude, and shifts.
$$f(x)=3 \hspace{.1em}\text{sin}\left(5x + \frac{3π}{4}\right) + 4$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{2π}{5}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{3π}{20}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
B
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{2π}{3}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{5π}{12}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
C
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{2π}{5}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\frac{3π}{20}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
D
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{2π}{5}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\frac{π}{4}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
E
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{4π}{3}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{5π}{24}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}5 \hspace{.1em}\text{Units}$$
Question 2 of 5Find the period, amplitude, and shifts.
$$f(x)=6 \hspace{.1em}\text{cos}\left(8x + \frac{π}{3}\right) + 4$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\text{Amplitude:}\hspace{.1em}6$$ $$\text{Period:}\hspace{.1em}\frac{π}{4}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\frac{π}{18}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
B
$$\text{Amplitude:}\hspace{.1em}6$$ $$\text{Period:}\hspace{.1em}π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{7π}{8}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}2 \hspace{.1em}\text{Units}$$
C
$$\text{Amplitude:}\hspace{.1em}6$$ $$\text{Period:}\hspace{.1em}\frac{π}{3}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{5π}{24}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
D
$$\text{Amplitude:}\hspace{.1em}6$$ $$\text{Period:}\hspace{.1em}\frac{π}{4}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{π}{24}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
E
$$\text{Amplitude:}\hspace{.1em}6$$ $$\text{Period:}\hspace{.1em}\frac{π}{4}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\frac{π}{24}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
Question 3 of 5Find the period, amplitude, and shifts.
$$f(x)=\frac{1}{2}\hspace{.1em}\text{sin}\left(\frac{x}{7}+ \frac{π}{2}\right) - 3$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\text{Amplitude:}\hspace{.1em}\frac{1}{2}$$ $$\text{Period:}\hspace{.1em}\frac{14π}{3}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\frac{35π}{3}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}3 \hspace{.1em}\text{Units}$$
B
$$\text{Amplitude:}\hspace{.1em}\frac{1}{2}$$ $$\text{Period:}\hspace{.1em}14π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\frac{7π}{2}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}3 \hspace{.1em}\text{Units}$$
C
$$\text{Amplitude:}\hspace{.1em}\frac{1}{2}$$ $$\text{Period:}\hspace{.1em}14π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{35π}{3}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}3 \hspace{.1em}\text{Units}$$
D
$$\text{Amplitude:}\hspace{.1em}\frac{1}{2}$$ $$\text{Period:}\hspace{.1em}\frac{7π}{4}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\frac{π}{24}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}3 \hspace{.1em}\text{Units}$$
E
$$\text{Amplitude:}\hspace{.1em}\frac{1}{2}$$ $$\text{Period:}\hspace{.1em}\frac{9π}{4}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{7π}{2}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}3 \hspace{.1em}\text{Units}$$
Question 4 of 5Find the period, amplitude, and shifts.
$$f(x)=3 \hspace{.1em}\text{sin}\left(7x - \frac{2π}{3}\right) - 4$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{2π}{5}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{π}{4}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
B
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{2π}{7}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{2π}{21}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
C
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{2π}{7}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\frac{2π}{21}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
D
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{2π}{7}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{2π}{9}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
E
$$\text{Amplitude:}\hspace{.1em}3$$ $$\text{Period:}\hspace{.1em}\frac{4π}{21}$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\frac{8π}{13}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}4 \hspace{.1em}\text{Units}$$
Question 5 of 5Find the transformation.
$$f(x)=4 \hspace{.1em}\text{sin}\left(7x - \frac{π}{4}\right) + 5$$
Finish »
Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
Starting with our basic sine graph, vertically compress by a factor of 1/3, horizontally compress by a factor of 1/3, shift left $π$/12, and shift up by 2
B
Starting with our basic sine graph, vertically stretch by a factor of 4, horizontally compress by a factor of 1/7, shift left $π$/28, and shift up by 5
C
Starting with our basic sine graph, vertically stretch by a factor of 4, horizontally compress by a factor of 1/7, shift right $π$/28, and shift up by 5
D
Starting with our basic sine graph, vertically stretch by a factor of 7, horizontally compress by a factor of 1/4, shift right $π$/16, and shift up by 5
E
Starting with our basic sine graph, vertically compress by a factor of 4, horizontally compress by a factor of 7, shift left $π$/28, and shift up by 5

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