Question 1 of 5Find the period, phase shift, vertical shift, and vertical asymptotes.
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A
$$\text{Period:}3π$$ $$\text{Phase Shift:}\text{Left}\frac{π}{6}$$ $$\text{Vertical Shift:}\text{Down}\hspace{.1em}2$$ $$\text{V.A.:}\hspace{.1em}x=\frac{π}{3}+ πn$$ $$\text{n is an integer}$$
B
$$\text{Period:}\frac{π}{3}$$ $$\text{Phase Shift:}\text{Right}\frac{π}{6}$$ $$\text{Vertical Shift:}\text{Up}\hspace{.1em}2$$ $$\text{V.A.:}\hspace{.1em}x=\frac{πn}{3}$$ $$\text{n is an integer}$$
C
$$\text{Period:}\frac{π}{3}$$ $$\text{Phase Shift:}\text{Right}\frac{3π}{2}$$ $$\text{Vertical Shift:}\text{Up}\hspace{.1em}7$$ $$\text{V.A.:}\hspace{.1em}x=\frac{2π}{3}+ \frac{πn}{3}$$ $$\text{n is an integer}$$
D
$$\text{Period:}3π$$ $$\text{Phase Shift:}\text{Right}\frac{2π}{3}$$ $$\text{Vertical Shift:}\text{Up}\hspace{.1em}3$$ $$\text{V.A.:}\hspace{.1em}x=\frac{πn}{6}$$ $$\text{n is an integer}$$
E
$$\text{Period:}\frac{π}{3}$$ $$\text{Phase Shift:}\text{Left}\frac{π}{12}$$ $$\text{Vertical Shift:}\text{Up}\hspace{.1em}2$$ $$\text{V.A.:}\hspace{.1em}x=\frac{πn}{3}$$ $$\text{n is an integer}$$
Question 2 of 5Find the period, phase shift, vertical shift, and vertical asymptotes.
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A
$$\text{Period:}\frac{π}{5}$$ $$\text{Phase Shift:}\text{Right}\frac{5π}{2}$$ $$\text{Vertical Shift:}\text{Down}\hspace{.1em}4$$ $$\text{V.A.:}\hspace{.1em}x=\frac{11π}{2}+ \frac{πn}{5}$$ $$\text{n is an integer}$$
B
$$\text{Period:}5π$$ $$\text{Phase Shift:}\text{Left}\frac{π}{6}$$ $$\text{Vertical Shift:}\text{Down}\hspace{.1em}4$$ $$\text{V.A.:}\hspace{.1em}x=\frac{π}{6}+ 5πn$$ $$\text{n is an integer}$$
C
$$\text{Period:}\frac{π}{5}$$ $$\text{Phase Shift:}\text{Right}\frac{π}{6}$$ $$\text{Vertical Shift:}\text{Down}\hspace{.1em}4$$ $$\text{V.A.:}\hspace{.1em}x=\frac{π}{6}+ \frac{πn}{5}$$ $$\text{n is an integer}$$
D
$$\text{Period:}\frac{π}{5}$$ $$\text{Phase Shift:}\text{Right}\frac{π}{6}$$ $$\text{Vertical Shift:}\text{Up}\hspace{.1em}\frac{1}{3}$$ $$\text{V.A.:}\hspace{.1em}x=\frac{π}{6}+ \frac{πn}{5}$$ $$\text{n is an integer}$$
E
$$\text{Period:}\frac{7π}{3}$$ $$\text{Phase Shift:}\text{Left}\frac{π}{6}$$ $$\text{Vertical Shift:}\text{Down}\hspace{.1em}4$$ $$\text{V.A.:}\hspace{.1em}x=\frac{14π}{3}+ \frac{7πn}{3}$$ $$\text{n is an integer}$$
Question 3 of 5Find the transformation.
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A
Starting with our basic cotangent graph, vertically stretch by a factor of 4, horizontally shrink by a factor of 1/3, shift left 4$π$, and shift down 1
B
Starting with our basic cotangent graph, vertically shrink by a factor of 1/4, horizontally stretch by a factor of 3, shift left 4$π$, and shift down 1
C
Starting with our basic cotangent graph, vertically stretch by a factor of 4, horizontally shrink by a factor of 1/3, shift left $\frac{4π}{3}$, and shift down 1
D
Starting with our basic cotangent graph, vertically stretch by a factor of 4, horizontally stretch by a factor of 3, shift right 4$π$, and shift down 1
E
Starting with our basic cotangent graph, vertically stretch by a factor of 4, horizontally stretch by a factor of 3, shift right $\frac{4π}{3}$, and shift down 1
Question 4 of 5Find the transformation.
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A
Starting with our basic tangent graph, vertically shrink by a factor of 1/2, horizontally shrink by a factor of 1/2, shift left $\frac{π}{8}$, and shift up 2
B
Starting with our basic tangent graph, vertically shrink by a factor of 1/2, horizontally stretch by a factor of 2, shift right $\frac{π}{8}$, and shift up 2
C
Starting with our basic tangent graph, vertically stretch by a factor of 2, horizontally stretch by a factor of 2, shift right $\frac{π}{8}$, and shift up 2
D
Starting with our basic tangent graph, vertically stretch by a factor of 2, horizontally stretch by a factor of 2, shift right $\frac{π}{4}$, and shift up 2
E
Starting with our basic tangent graph, vertically shrink by a factor of 1/2, horizontally shrink by a factor of 1/2, shift left $\frac{π}{4}$, and shift up 2
Question 5 of 5Find the transformation.
Select the Correct Answer Below: Correct! Not Correct!
A
Starting with our basic tangent graph, vertically shrink by a factor of 1/4, horizontally stretch by a factor of 8, shift right $\frac{π}{4}$, and shift down 3
B
Starting with our basic tangent graph, vertically shrink by a factor of 1/4, horizontally stretch by a factor of 8, shift left $\frac{π}{4}$, and shift down 3
C
Starting with our basic tangent graph, vertically shrink by a factor of 1/4, horizontally stretch by a factor of 8, shift right $\frac{π}{32}$, and shift down 3
D
Starting with our basic tangent graph, vertically shrink by a factor of 1/4, horizontally shrink by a factor of 1/8, shift right $\frac{π}{32}$, and shift down 3
E
Starting with our basic tangent graph, vertically stretch by a factor of 4, horizontally shrink by a factor of 1/8, shift left $\frac{π}{32}$, and shift down 3

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