Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Functions : High School: Functions

Study concepts, example questions & explanations for Common Core: High School - Functions

Create An Account

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 … 38 39 40 41 42 43 44 45 46 47 Next →

Example Question #4 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the period of the following function?

$y=\sin(4x)$

Possible Answers:

$\pi$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

Correct answer:

$\frac{\pi}{2}$

Explanation:

This question is testing one's ability to identify the periodicity of a trigonometric function. This requires the understanding of trigonometric functions and their graphical and algebraic characteristics.

For the purpose of Common Core Standards, "Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline" falls within the Cluster B of "Model Periodic Phenomena with Trigonometric Functions" concept (CCSS.MATH.CONTENT.HSF-TF.B.5).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

$\\F(x)=\textup{New function after shift} \\a=\textup{Amplitude} \\b=\textup{period}\rightarrow \frac{2\pi}{|B|} \\ \\c=\textup{Horizontal shift} \\ d=\textup{Vertical shift} \\f(x)=\textup{Trigonometric function}$

Step 2: Algebraically identify the period.

Given the function

$y=\sin(4x)$

identify the variables of the general form.

$\\f(x)=\sin \\a=1 \\b=4\rightarrow \frac{2\pi}{|4|}=\frac{\pi}{2} \\c=0 \\d=0$

Step 3: Graph the trigonometric function to verify.

The graph above verifies that the period of this function is $\frac{\pi}{2}$ because the flow of the graph only begins to repeat its cycle after $\frac{\pi}{2}$ units on the - axis.

Report an Error

Example Question #5 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the vertical shift of the function?

$f(x)=\sin(x)+\pi$

Possible Answers:

$\frac{\pi}{2}$

$\pi$

Correct answer:

$\pi$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the vertical shift.

Given the function

$y=\sin(x)+\pi$

identify the variables of the general form.

$\\f(x)=\sin \\a=1 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=0 \\d=\pi$

Step 3: Graph the trigonometric function to verify.

The graph above verifies that the vertical shift of the function is $\pi$ .

Report an Error

Example Question #6 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the vertical shift of the function?

$f(x)=\sin(x)-\pi$

Possible Answers:

$-\pi$

$\frac{\pi}{2}$

$2\pi$

$\pi$

Correct answer:

$-\pi$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the vertical shift.

Given the function

$y=\sin(x)-\pi$

identify the variables of the general form.

$\\f(x)=\sin \\a=1 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=0 \\d=-\pi$

Step 3: Graph the trigonometric function to verify.

The graph above verifies that the vertical shift of the function is $-\pi$ .

Report an Error

Example Question #7 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the horizontal shift of the function?

$f(x)=\sin(x-\pi)$

Possible Answers:

$\pi$

$\frac{\pi}{2}$

$-\pi$

Correct answer:

$\pi$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the horizontal shift.

Given the function

$y=\sin(x-\pi)$

identify the variables of the general form.

$\\f(x)=\sin \\a=1 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=\pi \\d=0$

Step 3: Graph the trigonometric function to verify.

The graph above verifies that the horizontal shift of the function is $\pi$ .

Report an Error

Example Question #8 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the horizontal shift of the function?

$f(x)=\sin(x+\pi)$

Possible Answers:

$\frac{\pi}{2}$

$-\pi$

$\pi$

$-\frac{\pi}{2}$

Correct answer:

$-\pi$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the horizontal shift.

Given the function

$y=\sin(x+\pi)$

identify the variables of the general form.

$\\f(x)=\sin \\a=1 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=-\pi \\d=0$

Step 3: Graph the trigonometric function to verify.

The graph above verifies that the horizontal shift of the function is $-\pi$ .

Report an Error

Example Question #9 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the amplitude of the following function?

$y=2\cos(x)$

Possible Answers:

$\pi$

$2\pi$

Correct answer:

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the amplitude.

Given the function

$y=2\cos(x)$

identify the variables of the general form.

$\\f(x)=\cos \\a=2 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=0 \\d=0$

Step 3: Graph the trigonometric function to verify.

The graph above verifies that the amplitude of this function is two because the range of the function on the graph goes from negative two to positive two meaning the distance from zero at its highest peak or lowest valley is two.

Report an Error

Example Question #10 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the period of the following function?

$y=\cos(2x)$

Possible Answers:

$\pi$

$2\pi$

$\frac{\pi}{2}$

Correct answer:

$\pi$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the period.

Given the function

$y=\cos(2x)$

identify the variables of the general form.

$\\f(x)=\cos \\a=1 \\b=2\rightarrow \frac{2\pi}{|2|}=\pi \\c=0 \\d=0$

Step 3: Graph the trigonometric function to verify.

Q10

The graph above verifies that the period of this function is $\pi$ because the flow of the graph only begins to repeat its cycle after $\pi$ units on the - axis.

Report an Error

Example Question #11 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the vertical shift of the function?

$f(x)=\cos(x)+\pi$

Possible Answers:

$\pi$

$\frac{\pi}{2}$

$-\pi$

Correct answer:

$\pi$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the vertical shift.

Given the function

$y=\cos(x)+\pi$

identify the variables of the general form.

$\\f(x)=\cos \\a=1 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=0 \\d=\pi$

Step 3: Graph the trigonometric function to verify.

Q11

The graph above verifies that the vertical shift of the function is $\pi$ .

Report an Error

Example Question #52 : Trigonometric Functions

What is the vertical shift of the function?

$f(x)=\cos(x)-\pi$

Possible Answers:

$\pi$

$-\pi$

$\frac{\pi}{2}$

Correct answer:

$-\pi$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the vertical shift.

Given the function

$y=\cos(x)-\pi$

identify the variables of the general form.

$\\f(x)=\cos \\a=1 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=0 \\d=-\pi$

Step 3: Graph the trigonometric function to verify.

Q12

The graph above verifies that the vertical shift of the function is $-\pi$ .

Report an Error

Example Question #1 : Restricting Domain Of Trigonometric Functions To Allow For Construction Of Inverse: Ccss.Math.Content.Hsf Tf.B.6

Find the exact value of the following statement.

$f(x)=\cos^{-1}(1)$

Possible Answers:

$\frac{\pi}{2}$

$2\pi$

$\frac{\pi}{3}$

$\pi$

$-\pi$

Correct answer:

$2\pi$

Explanation:

This question is testing ones ability to understand and identify inverses of trigonometric functions as they relate to the unit circle.

For the purpose of Common Core Standards, " Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed." concept (CCSS.MATH.CONTENT.HSF-TF.B.6). It is important to note that this standard is not directly tested on but is used for building a deeper understanding on trigonometric functions.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Since there is a trigonometric function raised to the negative one power, this question is talking about the inverse of the function. In other words, which angle on the unit circle results in a cosine equalling one?

$y=\cos^{-1}(a)\Rightarrow \cos(\theta)=a$

Therefore, theta needs to be solved for.

Step 2: Draw and label the unit circle.

Screen shot 2016 01 14 at 10.52.42 am

Step 3: Locate the angle that results in one for its cosine value.

Recall that

$(x,y)=(\cos(\theta),\sin(\theta))$

therefore look for the (x,y) that has x=1 . Looking at the unit circle from step 2, it is seen that at angle $2\pi$ the cosine equals one.

Thus,

$f(x)=\cos^{-1}(1)\Rightarrow f(x)=2\pi$

To verify the solution simply find the cosine of the angle theta.

$\cos(2\pi)=1\rightarrow\cos^{-1}(1)=2\pi$

Report an Error

← Previous 1 2 … 38 39 40 41 42 43 44 45 46 47 Next →

View Tutors

Sonu
Certified Tutor

Rajasthan Technical University Kota, Bachelor, Electrical.

View Tutors

Kevin
Certified Tutor

Washington State University, Bachelor of Science, Psychology. Washington State University, Bachelor in Arts, Elementary Schoo...

View Tutors

Anabel
Certified Tutor

UDELAR, Diploma, Chemistry. IPA, Bachelor of Education, Mathematics.

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Chicago, Computer Science Tutors in Washington DC, LSAT Tutors in Miami, GMAT Tutors in San Francisco-Bay Area, GMAT Tutors in Chicago, Computer Science Tutors in Denver, ISEE Tutors in Boston, Biology Tutors in Washington DC, French Tutors in Los Angeles, French Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in New York City, ISEE Courses & Classes in Chicago, Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Denver, GMAT Courses & Classes in Denver, SAT Courses & Classes in San Diego, LSAT Courses & Classes in Seattle, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Chicago, SSAT Courses & Classes in Miami

Popular Test Prep

LSAT Test Prep in Los Angeles, ACT Test Prep in Dallas Fort Worth, ACT Test Prep in New York City, SAT Test Prep in Los Angeles, LSAT Test Prep in Denver, ISEE Test Prep in Philadelphia, ACT Test Prep in Washington DC, GRE Test Prep in Houston, MCAT Test Prep in Chicago, GMAT Test Prep in Denver

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Common Core: High School - Functions : High School: Functions

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #4 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #5 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #6 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #7 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #8 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #9 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #10 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #11 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #52 : Trigonometric Functions

Example Question #1 : Restricting Domain Of Trigonometric Functions To Allow For Construction Of Inverse: Ccss.Math.Content.Hsf Tf.B.6

All Common Core: High School - Functions Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: