We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Introduction to Functions

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 10 … 28 29 Next →

Example Question #51 : Functions And Graphs

Squareroot

$\textup{What is the domain of }y=\sqrt{x}\textup{ ?}$

Possible Answers:

x>0

$x= all \:real \: numbers$

$x\geq0$

$y \neq0$

Correct answer:

$x\geq0$

Explanation:

You cannot take the square root of a negative number.

Report an Error

Example Question #52 : Functions And Graphs

Identity

$\textup{What is the domain of y = x ?}$

Possible Answers:

y>0

$x\geq0$

$y\neq0$

$y= all \:real \: numbers$

Correct answer:

$y= all \:real \: numbers$

Explanation:

The function includes all possible y-values (outputs). There is nothing you can put in for y that won't work.

Report an Error

Example Question #53 : Functions And Graphs

Parabola

$\textup{What is the range of }y=x^{2}\textup{ ?}$

Possible Answers:

$y= all \:real \: numbers$

x>0

y>0

$y\geq0$

Correct answer:

$y\geq0$

Explanation:

Squaring an input cannot produce a negative output.

Report an Error

Example Question #54 : Functions And Graphs

Cubing

$\textup{What is the range of }y=x^{3}\textup{ ?}$

Possible Answers:

$y\leq1$

y>0

$y= all \:real \: numbers$

$x= all \:real \: numbers$

Correct answer:

$y= all \:real \: numbers$

Explanation:

The function includes all possible y-values (outputs). There is nothing you can put in for y that won't work.

Report an Error

Example Question #55 : Functions And Graphs

Exponential

$\textup{What is the range of }y=2^{x}\textup{?}$

Possible Answers:

$x\geq0$

$y\geq0$

y>0

$y= all \:real \: numbers$

Correct answer:

y>0

Explanation:

A number taken to a power must be positive.

Report an Error

Example Question #56 : Functions And Graphs

Squareroot

$\textup{What is the range of } y=\sqrt{x}\textup{ ?}$

Possible Answers:

$y= all \:real \: numbers$

$x\neq0$

y>0

$y\geq0$

Correct answer:

$y\geq0$

Explanation:

The square root of any number cannot be negative.

Report an Error

Example Question #57 : Functions And Graphs

Absolutevalue

$\textup{What is the range of }y=\left | x\right |\textup{?}$

Possible Answers:

$y\geq0$

$y=\:all\:real\:numbers$

y>0

$x\geq0$

Correct answer:

$y\geq0$

Explanation:

The absolute value of a number cannot be negative.

Report an Error

Example Question #30 : Domain And Range

Determine the domain of the following function:

$y=\frac{x^2+6x-4}{x-5}$

Possible Answers:

$-\infty<x<5$ and $5<x<\infty$

$-\infty <x<\infty$

$x\le 16-2\sqrt{51}$ and $x \ge 2(8+\sqrt{51})$

$-\infty <x<0$ and $0<x<\infty$

$0\le x<\infty$

Correct answer:

$-\infty<x<5$ and $5<x<\infty$

Explanation:

The domain is all the possible values of . To determine the domain, we need to determine what values don't work for this equation. The only value that is not allowed for this equation is 5, since that would make the denominator have a value of , and you can not divide by . Therefore, the domain of this equation is:

$-\infty < x<5$ and $5<x<\infty$

Report an Error

Example Question #8 : How To Find The Domain Of A Function

Give the domain of the function:

$f(x) = \frac{x^{2} - 16}{x^{2}-6x+9}$

Possible Answers:

$\left \{ x | x \neq 3 \right \}$

$\left \{ x |x \neq -3 , x \neq 3 \right \}$

$\left \{ x | x\neq -4, x \neq 3, x\neq 4\right \}$

$\left \{ x |x \neq -3 \right \}$

$\left \{ x |x \neq -4 , x \neq 4 \right \}$

Correct answer:

$\left \{ x | x \neq 3 \right \}$

Explanation:

The domain of a rational function is the set of all values of for which the denominator is not equal to 0, so we set the denominator to 0 and solve for .

$x^{2} -6x + 9 = 0$

This is a quadratic function, so we factor the expression as (x+?)(x+?) , replacing the question marks with two numbers whose product is 9 and whose sum is . These numbers are -3,-3 , so

$x^{2} -6x + 9 = 0$

becomes

(x-3)(x-3) = 0 ,

or $(x-3)^{2} = 0$ .

This means that x-3=0 , or x = 3 .

Therefore, 3 is the only number excluded from the domain.

Report an Error

Example Question #9 : How To Find The Domain Of A Function

Give the domain of the function:

$f(x) = \frac{x^{2} - 4}{x^{2}-6x+8}$

Possible Answers:

$\left \{x | x \neq -2, x \neq 2\ \right \}$

$\left \{x | x \neq 2 \right \}$

The set of all real numbers.

$\left \{x | x \neq 2 ,x \neq 4 \right \}$

$\left \{x | x \neq -2, x \neq 2 ,x \neq 4 \right \}$

Correct answer:

$\left \{x | x \neq 2 ,x \neq 4 \right \}$

Explanation:

The domain of a rational function is the set of all values of for which the denominator is not equal to 0 (the value of the numerator is irrelevant), so we set the denominator to 0 and solve for to find the excluded values.

$x^{2}-6x+8 =0$

This is a quadratic function, so we factor the expression as (x+?)(x+?) , replacing the question marks with two numbers whose product is 8 and whose sum is . These numbers are -4,-2 , so

$x^{2}-6x+8 =0$

becomes

(x-2)(x-4) = 0

So either

x-2 = 0 , in which case x = 2 ,

or x-4 = 0 , in which case x = 4 .

Therefore, 2 and 4 are the only numbers excluded from the domain.

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 … 28 29 Next →

View Algebra 2 Tutors

Swagatika
Certified Tutor

Regional Institute of Education Bhubaneswar, Bachelor of Economics, Mathematics.

View Algebra 2 Tutors

Alena
Certified Tutor

Mogilevsky State Pedagogical Institute, Bachelor in Arts, Mathematics. Mogilevsky State Pedagogical Institute, Masters, Mathe...

View Algebra 2 Tutors

Jitendra
Certified Tutor

BHU, Bachelor, Mathematics.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Los Angeles, Computer Science Tutors in Boston, Calculus Tutors in New York City, LSAT Tutors in San Diego, GMAT Tutors in San Diego, Calculus Tutors in Miami, GMAT Tutors in Philadelphia, SSAT Tutors in Boston, GRE Tutors in Philadelphia, Reading Tutors in Chicago

Popular Courses & Classes

ACT Courses & Classes in Chicago, ACT Courses & Classes in Los Angeles, MCAT Courses & Classes in Miami, LSAT Courses & Classes in San Diego, ACT Courses & Classes in Houston, MCAT Courses & Classes in Houston, LSAT Courses & Classes in Miami, MCAT Courses & Classes in San Diego, ACT Courses & Classes in Seattle, SAT Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in Houston, ACT Test Prep in Seattle, GMAT Test Prep in Washington DC, ACT Test Prep in Los Angeles, MCAT Test Prep in New York City, ACT Test Prep in Chicago, LSAT Test Prep in San Diego, MCAT Test Prep in Denver, SAT Test Prep in Seattle, MCAT Test Prep in San Francisco-Bay Area

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

Algebra II : Introduction to Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #51 : Functions And Graphs

Example Question #52 : Functions And Graphs

Example Question #53 : Functions And Graphs

Example Question #54 : Functions And Graphs

Example Question #55 : Functions And Graphs

Example Question #56 : Functions And Graphs

Example Question #57 : Functions And Graphs

Example Question #30 : Domain And Range

Example Question #8 : How To Find The Domain Of A Function

Example Question #9 : How To Find The Domain Of A Function

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: