Creating Equations from Graphs (Sine Graph)

1) Which of the following equations matches a sine graph with amplitude 4 and period 2π?

Y = 4sin(x)

Y = sin(4x)

Y = sin(x/4)

Y = (1/4)sin(x)

2) Which of the following equations matches a sine graph with amplitude 1 and period π?

Y = 2sin(x)

Y = sin(2x)

Y = sin(x/2)

Y = sin(x) + 2

3) Which of the following equations matches a sine graph with amplitude 6, period 2π, and midline y = -2?

Y = sin(6x) - 2

Y = 6sin(2x) - 2

Y = 6sin(x) - 2

Y = 6sin(x + 2)

4) Which of the following equations matches a sine graph with amplitude 1/2 and period 4π?

Y = sin(2x)/2

Y = (1/2)sin(2x)

Y = (1/2)sin(x)

Y = (1/2)sin(x/2)

5) Which of the following equations matches a sine graph with amplitude 3, period 2π, and midline y = 5?

Y = sin(3x) + 5

Y = 3sin(x) + 5

Y = 3sin(x/5)

Y = 5 + sin(x/3)

6) Which of the following equations matches a sine graph with amplitude 2 and period π?

Y = 2sin(x/2)

Y = 2sin(2x)

Y = sin(2x)

Y = 2sin(x)

7) Which of the following equations matches a sine graph with amplitude 9, period 2π, and midline y = 4?

Y = sin(9x) + 4

Y = 9sin(x/4)

Y = 9sin(x) + 4

Y = 9sin(x + 4)

8) Which of the following equations matches a sine graph with amplitude 1, period 6π, and midline y = -1?

Y = sin(3x) - 1

Y = sin(x/6) - 1

Y = sin(6x) - 1

Y = sin(x/3) - 1

9) Which of the following equations matches a sine graph with amplitude 3/4 and period 2π?

Y = (3/4)sin(x)

Y = sin((3/4)x)

Y = sin(x) + 3/4

Y = (4/3)sin(x)

10) Which of the following equations matches a sine graph with amplitude 5, period 4π, and midline y = 2?

Y = 5sin(2x) + 2

Y = 5sin(x/2) + 2

Y = 2 + sin(5x)

Y = 5sin(x) + 2

11) Which of the following equations matches a sine graph with amplitude 1, period 2π, and midline y = 3?

Y = sin(x) + 3

Y = 3sin(x) + 1

Y = sin(3x) + 1

Y = sin(x + 3)

12) Which of the following equations matches a sine graph with amplitude 7, period π, and midline y = −4?

Y = 7sin(x/2) − 4

Y = 7sin(2x) − 4

Y = sin(7x) − 4

Y = 7sin(x) − 4

13) Which of the following equations matches a sine graph with amplitude 2, period 2π, and midline y = −6?

Y = 2sin(x) − 6

Y = sin(2x) − 6

Y = 2sin(x − 6)

Y = −6sin(x) + 2

14) Which of the following equations matches a sine graph with amplitude 1 and period 2π/5?

Y = sin(x/5)

Y = sin(5x)

Y = 5sin(x)

Y = (1/5)sin(x)

15) Which of the following equations matches a sine graph with amplitude 4 and period 12π?

Y = 4sin(6x)

Y = 4sin(x)

Y = 4sin(x/6)

Y = sin(x/6) + 4

16) Which of the following equations matches a sine graph with amplitude 1, period π, and midline y = 7?

Y = sin(x/2) + 7

Y = sin(x) + 7

Y = sin(7x) + 1

Y = sin(2x) + 7

17) Which of the following equations matches a sine graph with amplitude 5 and period 2π?

Y = 5sin(x)

Y = sin(5x)

Y = sin(x) + 5

Y = (1/5)sin(x)

18) Which one do you like?Which of the following equations matches a sine graph with amplitude 2, period 8π, and midline y = −3?

Y = 2sin(4x) − 3

Y = 2sin(x) − 3

Y = 2sin(x/4) − 3

Y = sin(x/4) − 3

19) Which of the following equations matches a sine graph with amplitude 1/2, period 2π, and midline y = 10?

Y = (1/2)sin(2x) + 10

Y = sin(0.5x) + 10

Y = (1/2)sin(x) + 10

Y = sin(x) + 0.5

20) Which of the following equations matches a sine graph with amplitude 3, period π, and midline y = 2?

Y = 3sin(x/2) + 2

Y = sin(3x) + 2

Y = 2 + sin(x/3)

Y = 3sin(2x) + 2