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

Example Question #41 : Introduction To Functions

What is the domain of the following function? Please use interval notation.

$y=\left | -x\right |$

Possible Answers:

$(-\infty ,\infty )$

$(-\infty ,0)$

$(0,\infty )$

Correct answer:

$(-\infty ,\infty )$

Explanation:

A basic knowledge of absolute value and its functions is valuable for this problem. However, if you do not know what the typical shape of an absoluate value function looks like, one can always plug in values and plot points.

Upon doing so, we learn that the -values (domain) are not restricted on either end of the function, creating a domain of negative infinity to postive infinity.

If we plug in -100000 for , we get 100000 for .

If we plug in 100000 for , we get 100000 for .

Additionally, if we plug in any value for , we will see that we always get a real, defined value for .

**Extra Note: Due to the absolute value notation, the negative (-) next to the is not important, in that it will always be made positive by the absolute value, making this function the same as $y=\left | x\right |$ . If the negative (-) was outside of the absolute value, this would flip the function, making all corresponding -values negative. However, this knowledge is most important for range, rather than domain.

Report an Error

Example Question #11 : Domain And Range

Use the following function and domain to answer this question

f(x)=.25x+.38

$\left \{ 2,4,6,8,10 \right \}$

Find the range of the function for the given doman. Are and directly or inversely related?

Possible Answers:

$\left \{ .88,1.38,1.88, 2.38, 2.88 \right \}, inverse$

$\left \{ .38, 1.88, 2.38, 3.88, 4.38 \right \}, inverse$

$\left \{ .38, 1.88, 2.38, 3.88, 4.38 \right \}, direct$

$\left \{ .88,1.38,1.88, 2.38, 2.88 \right \}, direct$

Correct answer:

$\left \{ .88,1.38,1.88, 2.38, 2.88 \right \}, direct$

Explanation:

To find the range, plug each value of the domain into the equation:

$f(2)=.25(2)+.38 = {\color{Red} .88}$

$f(4)=.25(4)+.38 = {\color{Red} 1.38}$

$f(6)=.25(6)+.38={\color{Red} 1.88}$

$f(8)=.25(8)+.38={\color{Red} 2.38}$

$f(10)=.25(10)+.38={\color{Red} 2.88}$

As the x-values increase, the y-values do as well. Therefore there is a ${\color{Red} direct}$ relationship

Report an Error

Example Question #12 : Domain And Range

Find the range of the function f(x): 4 + 0.75x for the domain $\left \{ {0,12,20,28} \right \}$ .

Possible Answers:

$\left \{ {4,13,19,25} \right \}$

$\left \{ {0,5,11,16} \right \}$

$\left \{ {0,9,16,21} \right \}$

$\left \{ {4,5,9,16} \right \}$

$\left \{ {0,4,12,16} \right \}$

Correct answer:

$\left \{ {4,13,19,25} \right \}$

Explanation:

The range of a function is the group of corresponding values for a given domain ( values). Plug each value into the function to find the range:

y_1=4+0.75(0)=4

y_2=4+0.75(12)=13

y_3=4+0.75(20)=19

y_4=4+0.75(28)=25

The range is $\left \{ {4,13,19,25} \right \}$ .

Report an Error

Example Question #11 : Domain And Range

A function has the following range:

$\left \{ 2,5,7,8 \right \}$

Which of the following CANNOT be the domain of the function.

Possible Answers:

$\left \{ 2,6,7,7 \right \}$

$\left \{ 1,2,3,4 \right \}$

$\left \{ 10,14,19,20 \right \}$

$\left \{ -2,-1,0,1 \right \}$

$\left \{ 21,19,17,15 \right \}$

Correct answer:

$\left \{ 2,6,7,7 \right \}$

Explanation:

Functions cannot have more than one value for each value. This means different numbers in the range cannot be assigned to the same value in the domain. Therefore, ${\color{Red} \left \{ 2,6,7,7 \right \}}$ cannot be the domain of the function.

Report an Error

Example Question #11 : Range And Domain

What is the range of the following function? Please use interval notation.

$y=-\left | x\right |$

Possible Answers:

$(0,-\infty )$

$(-\infty ,\infty )$

$(0,\infty )$

$(-\infty,0]$

Correct answer:

$(-\infty,0]$

Explanation:

Upon doing so, we learn that the -values (range) never surpass . This is because of the negative that is placed outside of the absolute value function. Meaning, for every value we plug in, we will always get a negative value for , except when x=0, y=0 .

With this knowledge, we can now confidently state the range as $(-\infty ,0]$

**Extra note: the negative sign outside of the absolute value is simply a transformation of $y=\left | x\right |$ , reflecting the function about the -axis.

Report an Error

Example Question #41 : Introduction To Functions

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

Possible Answers:

y>0

$x= all \:real \: numbers$

x>0

$y= all \:real \: numbers$

$x\neq0$

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

Report an Error

Example Question #42 : Introduction To Functions

Parabola

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

Possible Answers:

$x\geq0$

$x= all \:real \: numbers$

y>0

x>0

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

Report an Error

Example Question #43 : Introduction To Functions

Cubing

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

Possible Answers:

$y= all \:real \: numbers$

$x= all \:real \: numbers$

-1<x<1

x>0

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

Report an Error

Example Question #42 : Introduction To Functions

Absolutevalue

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

Possible Answers:

$x= all \:real \: numbers$

$x\neq0$

y>0

$x\geq0$

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

Report an Error

Example Question #43 : Introduction To Functions

Exponential

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

Possible Answers:

y>0

x>0

$x= all \:real \: numbers$

$x\neq0$

Correct answer:

$x= all \:real \: numbers$

Explanation:

All inputs are valid. There is nothing you can put in for x that won't work.

Report an Error

View Algebra 2 Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Algebra II Resources

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

Popular Subjects

GMAT Tutors in Boston, LSAT Tutors in San Diego, Spanish Tutors in Phoenix, Reading Tutors in Seattle, ISEE Tutors in New York City, Math Tutors in Houston, GMAT Tutors in Philadelphia, English Tutors in Philadelphia, SAT Tutors in Miami, MCAT Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Chicago, LSAT Courses & Classes in Phoenix, MCAT Courses & Classes in Los Angeles, ACT Courses & Classes in Houston, LSAT Courses & Classes in Seattle, LSAT Courses & Classes in Denver, GRE Courses & Classes in Denver, GMAT Courses & Classes in Atlanta, SSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ACT Test Prep in Houston, ACT Test Prep in Chicago, LSAT Test Prep in Los Angeles, ISEE Test Prep in Chicago, GRE Test Prep in New York City, LSAT Test Prep in Boston, SSAT Test Prep in Washington DC, LSAT Test Prep in Chicago, ISEE Test Prep in Los Angeles, GRE 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

Algebra II : Introduction to Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Introduction To Functions

Example Question #11 : Domain And Range

Example Question #12 : Domain And Range

Example Question #11 : Domain And Range

Example Question #11 : Range And Domain

Example Question #41 : Introduction To Functions

Example Question #42 : Introduction To Functions

Example Question #43 : Introduction To Functions

Example Question #42 : Introduction To Functions

Example Question #43 : Introduction To Functions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: