Transformations of Trig Graphs

Name:

Class:

Date:

Show your work for each problem.

1.
What is the amplitude of $y = -4\sin(2x) + 1$ ?
1. a) $5$
2. b) $-4$
3. c) $2$
4. d) $4$
2.
What is the period of $y = 3\cos(4x) - 2$ ? (Type pi for $\pi$ , like 3pi/4.)
3.
How is the graph of $y = \cos(x + \frac{\pi}{3})$ shifted compared with $y = \cos(x)$ ?
1. a) $\frac{\pi}{3}$ down
2. b) $\frac{\pi}{3}$ to the right
3. c) $\frac{\pi}{3}$ to the left
4. d) $\frac{\pi}{3}$ up
4.
The midline of $y = 2\sin(x - \pi) + 5$ is the line $y = D$ . What is $D$ ?
5.
Find the maximum and the minimum of $y = 3\sin(x) + 2$ .
6.
For $y = \sin(4x)$ , find the period, the key point step and the x-value of the first maximum after $x = 0$ . (Type pi for $\pi$ , like 3pi/4.)
7.
What is the phase shift of $y = \sin(2x - \frac{\pi}{2})$ ?
1. a) $\frac{\pi}{4}$ to the left
2. b) $\frac{\pi}{4}$ to the right
3. c) $\frac{\pi}{2}$ to the right
4. d) $\pi$ to the right
8.
For $y = -2\cos(x) + 3$ , find the amplitude, the maximum, the minimum and the y-value at $x = 0$ .
9.
The key points of $y = \sin(2(x - \frac{\pi}{6}))$ start at $x = \frac{\pi}{6}$ . What is the x-value of the maximum (the second key point)? (Type pi for $\pi$ , like 3pi/4.)
10.
Use the key points of $y = 3\sin(x - \frac{\pi}{2}) - 1$ to find its first maximum and its minimum value. (Type pi for $\pi$ , like 3pi/4.)
11.
Rewrite $y = \cos(3x + \pi)$ in the form $y = \cos(B(x - C))$ and find the phase shift and the period. (Type pi for $\pi$ , like -3pi/4.)
12.
Which equation has amplitude $2$ , period $\pi$ and midline $y = -1$ ?
1. a) $y = 2\sin(\frac{1}{2}x) - 1$
2. b) $y = 2\sin(\pi x) - 1$
3. c) $y = 2\sin(2x) - 1$
4. d) $y = -\sin(2x) + 2$
13.
Find the key point y-values of $y = -2\sin(x) + 1$ at $x = 0$ , $\frac{\pi}{2}$ , $\pi$ and $\frac{3\pi}{2}$ .
14.
Graph $y = 4\cos(\frac{1}{2}(x - \frac{\pi}{2})) - 1$ with key points: find the period, the step, the x-value of the minimum and the minimum value. (Type pi for $\pi$ , like 3pi/4.)
15.
For $y = 3\sin(2x + \frac{\pi}{3}) + 1$ , find where the cycle starts, the step and the first maximum. (Type pi for $\pi$ , like -3pi/4.)
16.
For $y = -3\sin(\frac{\pi}{4}(x - 1)) + 2$ , what is the x-value of the first minimum to the right of $x = 1$ ?
17.
The graph of $y = \sin(x)$ is first shifted $\frac{\pi}{2}$ to the right and THEN compressed horizontally by the factor $2$ . Which equation results?
1. a) $y = \sin(2(x - \frac{\pi}{2}))$
2. b) $y = \sin(2(x - \frac{\pi}{4}))$
3. c) $y = \sin(\frac{1}{2}(x - \frac{\pi}{2}))$
4. d) $y = \sin(\frac{x}{2} - \frac{\pi}{2})$
18.
What is the value of $y = 5\cos(2(x + \frac{\pi}{8})) - 2$ at $x = \frac{\pi}{8}$ ?