AnswersAlgebra 2 MP 234 CHSModeling with Periodic Functions

Modeling with Periodic Functions — Unit test Answers

25 verified answers1 views
21
Free Preview

Which of the following is true for f(x) = 5cos(x) +1?

A
The period of the function is .
Option A
B
The function has an amplitude of 2.5.
C
A zero of the function is .
Option C
D
The range of the function is the set of real numbers .
Option D
22
Free Preview

Francesca drew point (–2, –10) on the terminal ray of angle , which is in standard position. She found values for the six trigonometric functions using the steps below.Step 1Step 2 Step 3Which of the following explains whether all of Francesca’s work is correct?

Question illustration
A
Each step is correct because she plotted the point, drew a line to the x-axis to form a right triangle, used the Pythagorean theorem to find the hypotenuse, and finally wrote the correct ratios for all six functions.
B
She made her first error in step 1 because she should have drawn the line to the y-axis to form the right triangle.
C
She made her first error in step 2 because she should have used a negative value for r.
D
She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.
23

What are all the exact solutions of on the interval ? Give your answer in radians.

Question illustration
A
and
Option A
B
mc013-5.jpg
Option B
C
mc013-6.jpg
Option C
D
and
Option D
24

A rider boards a Ferris wheel 10 feet above ground level. The diameter of the Ferris wheel is 50 feet and the wheel completes one full rotation every 24 seconds. Which graph represents the relationship between time and height off the ground?

A
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It increases through the y-axis. Its cycle is 0.4 x.
Option A
B
On a coordinate plane, a curve starts at (0, 60). It has a maximum at y = 60 and a minimum at y = 10. It decreases through the y-axis. Its cycle is 0.4 x.
Option B
C
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It increases through the y-axis. Its cycle is 0.8 x.
Option C
D
On a coordinate plane, a curve starts at (0, 10). It has a maximum at y = 60 and a minimum at y = 10. It decreases through the y-axis. Its cycle is 0.8 x.
Option D
25

Throughout the day, the depth of water at the end of a dock varies with the tides. The function represents the height, in feet, of the water t hours after midnight.Which graph shows the height of the water at the dock at any time after midnight?

Question illustration
A
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It decreases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 13 feet.
Option A
B
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It increases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 13 feet.
Option B
C
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, 5). It increases through the y-axis. It has a minimum of y = 2 and a maximum of y =12. It goes through 1 cycle in 7 feet.
Option C
D
On a coordinate plane, feet is on the x-axis and depth is on the y-axis. A curve starts at (0, negative 2). It increases through the y-axis. It has a minimum of y = negative 5 and a maximum of y =5. It goes through 1 cycle in 13 feet.
Option D

Did you find these answers helpful?

More from this Course

Quiz
15 verified answers

Unit Test

Quiz
15 verified answers

Unit Test

Quiz
14 verified answers

Simplifying Rational Expressions

Modeling with Periodic Functions — Unit test…