algebra 2b - unit 4: trigonometric functions

what is the frequency of the function? https://cdstools.flipswitch.com/asset/media/1239660

2

examine the graph of the function f(x) = 2 cos(x). which is the graph of f(x) and the translation g(x) = f(x + π/4)

https://cdstools.flipswitch.com/asset/media/1240047

examine the graph of the function f(x) = 3 cos(x). which is the graph of f(x) and the translation g(x) = f(x) + 2?

https://cdstools.flipswitch.com/asset/media/1240052

examine the graph of the function f(x) = 2 sin(3x). which is the graph of f(x) and the translation g(x) = f(1/3x)?

https://cdstools.flipswitch.com/asset/media/1240067

what is the period of the tangent function? cdstools.flipswitch.com/asset/media/1239808

pi/2

which rule represents the graph of the function? https://cdstools.flipswitch.com/asset/media/1239530

f(x) = 3 sin(2x) + 1

what is the period of the function? https://cdstools.flipswitch.com/asset/media/1239659

p = pi

what is the period of the function? https://cdstools.flipswitch.com/asset/media/1239640

p = pi/2

lesson 20

transformations of trigonometric functions

which equation represent vertical asymptotes of the function shown?

x = pi/2 x = 3pi/2

examine the graph. https://cdstools.flipswitch.com/asset/media/1239537 what is the midline of the function?

y = 1

what is the rule that represents the function in the graph? https://cdstools.flipswitch.com/asset/media/1239669

y = 5 cos(x) + 3

what is the rule that represents the function in the graph? https://cdstools.flipswitch.com/asset/media/1239651

y = cos(5x) - 2

which equation represents the function in the graph? cdstools.flipswitch.com/asset/media/1239817

y = tan(1/4x)

which equation represents the function in the graph? cdstools.flipswitch.com/asset/media/1239808

y = tan(2x)

what is the period of the function? https://cdstools.flipswitch.com/asset/media/1239641

2pi/3

which graph represents y = tan(1/2x)?

cdstools.flipswitch.com/asset/media/1239804

which graphs represent tangent functions? select all that apply.

cdstools.flipswitch.com/asset/media/1239804 cdstools.flipswitch.com/asset/media/1239803

which graph represents y = tan (4x)?

cdstools.flipswitch.com/asset/media/1239810

the height of a single car on a ferris wheel is modeled by a cosine function. the car completes 4 whole rotations in a time period of 2π minutes. which function rule could model this situation?

f(x) = -106 cos(4x) + 106

examine the graph. https://cdstools.flipswitch.com/asset/media/1239519 what is the frequency of the function?

1/2

what is the amplitude of the function? https://cdstools.flipswitch.com/asset/media/1239639

3

which graph represents the function rule y = 4 cos(x) - 2?

https://cdstools.flipswitch.com/asset/media/1239665

lesson 17

graphs of cosine functions

examine the graph. https://cdstools.flipswitch.com/asset/media/1239515 what is the amplitude of the function?

2

the function that represents the location of the arrow is f(x) = 2 cos(8πx) + 2, where x represents time in seconds, and f(x) represents the vertical distance in inches that the arrow is from the lowest point on the yo-yo. what is the width of the yo-yo?

4 inches

examine the graph. https://cdstools.flipswitch.com/asset/media/1239513 what is the midline of the function?

y = 2

a certain sine function completes 2 cycles over the interval (0, 2π]. which function rule could model this situation?

f(x) = sin(2x)

lesson 16

graphs of sine functions

examine the graph. https://cdstools.flipswitch.com/asset/media/1239517 what is the frequency of the function?

2

a certain cosine function has a midline at y = 1. which function rule could model this situation?

f(x) = 2 cos(x) + 1

what is the period of the tangent function shown? cdstools.flipswitch.com/asset/media/1239813

3pi/4

what is the frequency of the function? https://cdstools.flipswitch.com/asset/media/1239642

6

what happens when the function f(x) = cos⁡(x) is transformed by the rule g(x) = f(x + 2)?

f(x) is translated 2 units to the left

the graph shows f(x) = 2 cos(3x) and the transformation g(x). for the transformation rule in the form, replacing which variable with what number will result in the transformation displayed in the graph?

replace a with 2

what is the midline of the function? https://cdstools.flipswitch.com/asset/media/1239658

y = 2

what is the midline of the function? https://cdstools.flipswitch.com/asset/media/1239638

y = 3

examine the graph. https://cdstools.flipswitch.com/asset/media/1239516 what is the frequency of the function?

4

examine the graph of the function f(x) = tan(x). which is the graph of f(x) and the translation g(x) = f(x) - 3?

https://cdstools.flipswitch.com/asset/media/1240057

which graph represents the function rule y = 2 cos(6x) + 4

https://cdstools.flipswitch.com/asset/media/1239647

which equation represents the function in the graph? cdstools.flipswitch.com/asset/media/1239811

y = tan(3/4x)

examine the graph. https://cdstools.flipswitch.com/asset/media/1239518 what is the period of the function?

π

which trigonometric function has 6 x-intercepts over the interval (0, 2π]?

f(x) = 4 cos(3x) + 2

a certain cosine function has an amplitude of 7. which function rule could model this situation?

f(x) = 7 cos(x) + 4

a certain cosine function completes 6 cycles over the interval [0, 2π]. which function rule could model this situation?

f(x) = cos(6x)

the graph shows f(x) = 5 sin⁡(x) + 2 and the transformation g(x). 1. what is the transformation rule that makes f(x) become g(x)? 2. what is the function rule of g(x)?

g(x) = f(2x) g(x) = 5 sin(2x) + 2

what is the graph of sin(2x) - 3?

https://cdstools.flipswitch.com/asset/media/1239524

examine the graph. https://cdstools.flipswitch.com/asset/media/1239519 what is the period of the function?

4π

what happens when the function f(x) = sin⁡(x) is transformed by the rule g(x) = 4 f(x)?

f(x) is stretched away from the x-axis by a factor of 4.

a spinning top can be represented by a sine function. the top completes 12 whole rotations in a time period of 2π seconds. which function rule could model this situation?

f(x) = sin(12x)

jackson takes a marker and draws an arrow at the top of his yo-yo, pointing it toward the string when it is all wound up. the location of the arrow on the yo-yo can be represented by a cosine function. the function that represents the location of the arrow is f(x) = 2 cos(8πx) + 2, where x represents time in seconds, and f(x) represents the vertical distance in inches that the arrow is from the lowest point on the yo-yo. how many times does the yo-yo rotate in 11 second?

4 times

which equations represent vertical asymptotes of the function? select all that apply. cdstools.flipswitch.com/asset/media/1239808

x = pi/4 x = 3pi/4 x = 7pi/4

what is the rule that represents the function in the graph? https://cdstools.flipswitch.com/asset/media/1239670

y = 4 cos(7x) - 1

which equation represents the function in the graph? cdstools.flipswitch.com/asset/media/1239803

y = tan(3x)

which rule represents the graph of the function? https://cdstools.flipswitch.com/asset/media/1239528

f(x) = 2 sin(4x) + 3

the graph shows f(x) = 3 cos(2x) - 2 and the transformation g(x). if a translation did not occur. 1. what is the transformation rule that makes f(x) become g(x)? 2. what is the function rule of g(x)?

g(x) = -f(x) g(x) = -3 cos(2x) + 2

which rule represents the graph of the function? https://cdstools.flipswitch.com/asset/media/1239529

f(x) = 3 sin(x) - 1

which rule represents the graph of the function? https://cdstools.flipswitch.com/asset/media/1239542

f(x) = sin(5x) + 3

the graph shows f(x) = 3 cos(2x) - 2 and the transformation g(x). 1. what is the transformation rule that makes f(x) become g(x)? 2. what is the function rule of g(x)?

g(x) = f(x) + 3 g(x) = 3 cos(2x) + 1

lesson 18

graphs of tangent functions

which are graphs of sine functions? select all that apply.

https://cdstools.flipswitch.com/asset/media/1239532 https://cdstools.flipswitch.com/asset/media/1239533 https://cdstools.flipswitch.com/asset/media/1239531

which is the graph of sin(2x)?

https://cdstools.flipswitch.com/asset/media/1239538

which graphs represent cosine functions? select all that apply.

https://cdstools.flipswitch.com/asset/media/1239655 https://cdstools.flipswitch.com/asset/media/1239653 https://cdstools.flipswitch.com/asset/media/1239654

which graph represents the function rule y = 2 cos(3x) + 6?

https://cdstools.flipswitch.com/asset/media/1239661

examine the graph. https://cdstools.flipswitch.com/asset/media/1239536 what is the amplitude of the function?

4

what is the amplitude of the function? https://cdstools.flipswitch.com/asset/media/1239638

4

a certain sine function has a midline at y = 3. which function rule could model this situation?

f(x) = sin(x) + 3

which are graphs of sine functions? select all that apply.

https://cdstools.flipswitch.com/asset/media/1239510 https://cdstools.flipswitch.com/asset/media/1239507

which is the graph of 2 sin(3x) + 4?

https://cdstools.flipswitch.com/asset/media/1239520

which graphs represent cosine functions? select all that apply.

https://cdstools.flipswitch.com/asset/media/1239634 https://cdstools.flipswitch.com/asset/media/1239633

which graph represents the function rule y = 4 cos(2x) − 1?

https://cdstools.flipswitch.com/asset/media/1239643

lesson 19

modeling with trigonometric functions

examine the graph of the function f(x) = 4 cos(x). which is the graph of f(x) and the translation g(x) = 2 f(x)?

https://cdstools.flipswitch.com/asset/media/1240062

what is the rule that represents the function in the graph? https://cdstools.flipswitch.com/asset/media/1239652

y = 3 cos(4x)

beginning in the middle of summer, the average temperature for a certain year in phoenix could approximately be modeled by the function f(x) = 26 cos⁡(0.0055πx) + 89, where x represents the number of days since the middle of the summer, and f(x) represents the average temperature in degrees fahrenheit. what was the highest average temperature in phoenix that year (approximately)?

115

examine the graph. https://cdstools.flipswitch.com/asset/media/1239514 what is the amplitude of the function?

3

which rule represents the graph of the function? https://cdstools.flipswitch.com/asset/media/1239543

f(x) = 2 sin(4x)

carlos has a nail in his car tire. the tire is not flat, but he's on his way to get it fixed. he's driving at a constant speed, and the diameter of the tire is 3 feet. which rule could model the height of the nail from the ground?

f(x) = 1.5 cos(16πx) + 1.5

what happens when the function f(x) = cos⁡(x) is transformed by the rule g(x) = f(3x)?

f(x) is compressed toward the y-axis by a factor of 1/3.

what happens when the function f(x) = 3 cos⁡(x) is transformed by the rule g(x) = f(−x)?

f(x) is reflected over the y-axis.

what happens when the function f(x) = sin⁡(x) is transformed by the rule g(x) = f(x) − 4?

f(x) is translated down 4 units

examine the graph. https://cdstools.flipswitch.com/asset/media/1239516 what is the period of the function?

pi/2