Creating Equations from Graphs (Cosine Graph)

1) Which of the following equations matches a cosine graph with amplitude 4, period 2π, midline y = 0, and a maximum at x = 0?

Y = cos(4x)

Y = (1/4)cos(x)

Y = 4cos(x)

Y = cos(x/4)

2) Which of the following equations matches a cosine graph with amplitude 1, period π, midline y = 0, and a minimum at x = 0?

Y = cos(2x)

Y = -cos(2x)

Y = cos(x/2)

Y = cos(2x) + 1

3) Which of the following equations matches a cosine graph with amplitude 6, period 2π, midline y = -2, and a maximum at x = 0?

Y = 6cos(2x) - 2

Y = cos(6x) - 2

Y = 6cos(x + 2) - 2

Y = 6cos(x) - 2

4) Which of the following equations matches a cosine graph with amplitude 1/2, period 4π, and midline y = 0?

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

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

Y = cos(x/2)

Y = (1/2)cos(x)

5) Which of the following equations matches a cosine graph with amplitude 3, period 2π, midline y = 5, and a maximum at x = 0?

Y = 3cos(x/5)

Y = 3cos(x + 5) + 5

Y = 3cos(x) + 5

Y = cos(3x) + 5

6) Which of the following equations matches a cosine graph with amplitude 2, period π, midline y = 0, and y-intercept 2?

Y = 2cos(2x)

Y = -2cos(2x)

Y = 2cos(x/2)

Y = cos(2x)

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

Y = 9cos(2x) + 4

Y = cos(9x) + 4

Y = 9cos(x - 1) + 4

Y = 9cos(x) + 4

8) Which of the following equations matches a cosine graph with amplitude 1, period 6π, midline y = -1, and a maximum at x = 0?

Y = cos(3x) - 1

Y = cos(x/3) - 1

Y = cos(6x) - 1

Y = cos(x/6) - 1

9) Which of the following equations matches a cosine graph with amplitude 3/4, period 2π, and midline y = 0?

Y = (3/4)cos(x)

Y = cos((3/4)x)

Y = cos(x) + 3/4

Y = (4/3)cos(x)

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

Y = 2 + cos(5x)

Y = 5cos(x) + 2

Y = 5cos(x/2) + 2

Y = 5cos(2x) + 2

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

Y = 3cos(x) + 1

Y = cos(x) + 3

Y = cos(3x) + 1

Y = cos(x + 3)

12) Which of the following equations matches a cosine graph with amplitude 7, period π, midline y = −4, and a minimum at x = 0?

Y = 7cos(2x) − 3

Y = 7cos(2x) − 4

Y = −7cos(x/2) − 4

Y = −7cos(2x) − 4

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

Y = 2cos(x) − 6

Y = cos(2x) − 6

Y = 2cos(2x) − 6

Y = 2cos(x) + 6

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

Y = cos(x/5)

Y = cos(5x)

Y = 5cos(x)

Y = (1/5)cos(x)

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

Y = 4cos(6x)

Y = 4cos(x)

Y = 4cos(x/6)

Y = cos(x/6) + 4

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

Y = cos(x/2) + 7

Y = cos(x) + 7

Y = cos(7x) + 1

Y = cos(2x) + 7

17) Which of the following equations matches a cosine graph with amplitude 5, period 2π, and midline y = 0?

Y = 5cos(x)

Y = cos(5x)

Y = cos(x) + 5

Y = (1/5)cos(x)

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

Y = 2cos(4x) − 3

Y = 2cos(x) − 3

Y = 2cos(x/4) − 3

Y = cos(x/4) − 3

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

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

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

Y = cos(0.5x) + 10

Y = cos(x) + 0.5

20) Which of the following equations matches a cosine graph with amplitude 3, period π, midline y = 2, and a minimum at x = 0?

Y = 3cos(x/2) + 2

Y = cos(3x) + 2

Y = 2 + cos(x/3)

Y = −3cos(2x) + 2