Vertical Shift

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Show your work for each problem.

1.
What is the midline of $y = 4\sin(x) - 3$ ?
1. a) $y = 4$
2. b) $y = -3$
3. c) $y = 0$
4. d) $y = 3$
2.
Which equation shifts $y = \cos(x)$ up by 5 units?
1. a) $y = \cos(x) + 5$
2. b) $y = 5\cos(x)$
3. c) $y = \cos(x + 5)$
4. d) $y = \cos(x) - 5$
3.
What is the maximum value of $y = 2\sin(x) + 5$ ?
4.
The midline of $y = \cos(x) - 6$ is $y = \square$ . What number goes in the box?
5.
What is the range of $y = 2\cos(x) + 3$ ?
1. a) $[3, 5]$
2. b) $[-1, 5]$
3. c) $[-2, 2]$
4. d) $[1, 5]$
6.
For $y = 3\cos(x) + 1$ , find the midline value, the amplitude, the maximum and the minimum.
7.
The graph of $y = \sin(x)$ is shifted down by 3 units. Find the new midline, maximum and minimum.
8.
What is the minimum value of $y = -4\cos(x) + 1$ ?
9.
What is the maximum value of $y = -3\sin(x) + 1$ ?
1. a) $-4$
2. b) $1$
3. c) $4$
4. d) $-2$
10.
A sine wave has a maximum of $8$ and a minimum of $-2$ . Find D and the amplitude $|A|$ .
11.
A wave swings between a maximum of $10$ and a minimum of $2$ . Its midline is $y = \square$ . What number goes in the box?
12.
Find the range of $y = -2\sin(x) - 1$ .
13.
The temperature in a town is modeled by $T(t) = 5\cos\left(\frac{\pi}{12}t\right) + 15$ in °C. Find the average temperature, the highest and lowest temperature, and the difference between them.
14.
A wave has a maximum of $7$ and a minimum of $-1$ . Which equation could describe it?
1. a) $y = 4\sin(x) - 3$
2. b) $y = 8\sin(x) + 3$
3. c) $y = 4\sin(x) + 3$
4. d) $y = 3\sin(x) + 4$
15.
A sinusoid has midline $y = -2$ and a maximum of $3$ . What is its minimum?
16.
A Ferris wheel has a diameter of 30 m and its center is 18 m above the ground. A seat starts at the bottom, and one turn takes 12 minutes, so $h(t) = -15\cos\left(\frac{\pi}{6}t\right) + 18$ . Analyze the model.
17.
At a harbor, high tide is 9.4 m and low tide is 1.6 m. Find the midline D and the amplitude $|A|$ of a tide model.
18.
The function $y = A\sin(x) + D$ with $A > 0$ has range $[-6, 2]$ . Find $D$ and $A$ , then the value of $y$ at $x = \frac{7\pi}{6}$ .