We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Algebraic Functions

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Functions

Solve for :

$3x^{2}-18x+24=0$

Possible Answers:

$x=2,\,3$

$x=2,\,4$

$x=-1,\,-6$

$x=-6,\,1$

$x=-2,\,4$

Correct answer:

$x=2,\,4$

Explanation:

To find , we must factor the quadratic function:

$3x^{2}-18x+24=0$

$3(x^{2}-6x+8)=0$

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

$x-4=0\, and \, x-2=0$

$x=4\,and\,2$

Report an Error

Example Question #241 : Grade 8

Solve for :

$2x^{2}-10x-28=0$

Possible Answers:

$x=2\,and\,x=-5$

$x=2\,and\,x=-7$

$x=-1\,and\,x=5$

$x=-2\,and\,x=5$

$x=-2\,and\,x=7$

Correct answer:

$x=-2\,and\,x=7$

Explanation:

To find , we want to factor the quadratic function:

$2x^{2}-10x-28=0$

$2(x^{2}-5x-14)=0$

2(x-7)(x+2)=0

$x-7=0\,and\,x+2=0$

$x=7\:and\:-2$

Report an Error

Example Question #1 : How To Find The Domain Of A Function

$\textup{What is the domain of the function }f(x)=\frac{x^{2}}{\sqrt{x+2}}?$

Possible Answers:

x>2

$x\geq-2$

x>-2

$x\geq-2$

x=-2

Correct answer:

x>-2

Explanation:

Report an Error

Example Question #2 : How To Find The Domain Of A Function

Define $f (x) = \sqrt[3]{\frac{100-x}{1,000-x}}$

What is the domain of ?

Possible Answers:

All real numbers except 1000

All real numbers except and

All real numbers except

All real numbers except 100 and 1000

All real numbers except , , 100 and 1000

Correct answer:

All real numbers except 1000

Explanation:

Every real number has a real cube root, so the radical does not restrict the domain of . The denominator of the expression does restrict the domain, however, in that it cannot be equal to 0. This happens only if:

1,000-x = 0 or, equivalently, x = 1,000 . Therefore, 1000 is the only real number not in the domain of .

Report an Error

Example Question #3 : How To Find The Domain Of A Function

Find the domain of the following function:

$\sqrt[3]{x^{3} - 2x}$

Possible Answers:

$x^{2}> 2$

$\left \{ x|-\infty< x< \infty \right \}$

$x=\sqrt{2}$

$x^{2}\nleqslant 2$

$x\neq 2$

Correct answer:

$\left \{ x|-\infty< x< \infty \right \}$

Explanation:

The expression under the radical is defined for all real values of since the index of the radical is 3.

Report an Error

Example Question #1 : How To Find The Domain Of A Function

Find the range of

$y=\sqrt{x-5}$

Possible Answers:

$\left \{ y\ |\ 0\leq y< \infty \right \}$

$\left \{ y\ |\ -\infty < y\leq 5 \right \}$

$\left ( x\ |\ 5\leq x< \infty \right )$

$\left \{ y\ |\ 0\leq y\leq 5 \right \}$

$\left \{ y\ |\ -\infty < y< \infty \right \}$

Correct answer:

$\left \{ y\ |\ 0\leq y< \infty \right \}$

Explanation:

Since the expression under the radical must be greater than or equal to zero, hence when x=5 , the f(x)=0 . Thereafter the f(x) is an increasing function.

Report an Error

Example Question #2 : How To Find The Domain Of A Function

You are given a relation that comprises the following five points:

$\left \{(1,2), (3,N), (5,4), (N+3, 9), (2N-1, 10) \right \}$

For which value of is this relation a function?

Possible Answers:

N = 4

N = - 2

N = 0

N = 2

The relation is not a function for any of these values of .

Correct answer:

N = 4

Explanation:

A relation is a function if and only if no -coordinate is paired with more than one -coordinate. We test each of these four values of to see if this happens.

N = - 2 :

The points become:

(1,2), (3,-2), (5,4), (1, 9), (-5, 10)

Since -coordinate 1 is paired with two -coordinates, 2 and 9, the relation is not a function.

N = 0 :

The points become:

(1,2), (3,0), (5,4), (3, 9), (-1, 10)

Since -coordinate 3 is paired with two -coordinates, 0 and 9, the relation is not a function.

N = 2 :

The points become:

(1,2), (3,2), (5,4), (5, 9), (3, 10)

Since -coordinates 3 and 5 are each paired with two different -coordinates, the relation is not a function.

N = 4 :

The points become:

(1,2), (3,4), (5,4), (7, 9), (9, 10)

Since each -coordinate is paired with one and only one -coordinate, the relation is a function. N = 4 is the correct choice.

Report an Error

Example Question #3 : How To Find The Domain Of A Function

Find the domain of the following function:

$f(x)=\sqrt{x+1}$

Possible Answers:

Domain can't be determined

$x\geq -1$

$x\geq 1$

$x\leq 1$

$x\leq -1$

Correct answer:

$x\geq -1$

Explanation:

Finding the domain is like finding out what possible values you can plug in without getting an error message on your calculator. We are given the function:

$f(x)=\sqrt{x+1}$

To find the domain, first, know that you can't take the square root of a negative number. It turns out that the minimum number you can take the square root of is zero. Any number above zero, everything is good. Therefore, x+1 can equal 0 or above. This is written as an inequality as:

$x+1\geq 0$

Solve for by subtracting 1 on both sides

$x+1-1\geq 0-1$

$x\geq -1$

So that's our domain!

Report an Error

Example Question #1 : Domain And Range

Give the domain of the function below.

$f(x) = \frac{1}{\sqrt{x^{2}+1}}$

Possible Answers:

$\left \{ x | x< -1\; or \; x> 1\right \}$

$\left \{x| -1<x<1 \right \}$

$\left \{ x | x\neq -1\right \}$

$\left \{ x | x\neq 1\right \}$

$\mathbb{R}$

Correct answer:

$\mathbb{R}$

Explanation:

The domain is the set of possible value for the variable. We can find the impossible values of by setting the denominator of the fractional function equal to zero, as this would yield an impossible equation.

$\sqrt{x^2+1}=0$

Now we can solve for .

x^2+1=0

x^2=-1

There is no real value of that will fit this equation; any real value squared will be a positive number.

The radicand is always positive, and $f(x) = \frac{1}{\sqrt{x^{2}+1}}$ is defined for all real values of . This makes the domain of the set of all real numbers.

Report an Error

Example Question #4 : How To Find The Domain Of A Function

What is the domain of the function $f(x)=\frac{2x}{x-2}$ ?

Possible Answers:

$\left ( -\infty ,0 \right )\cup \left ( 0,2 \right )\cup \left ( 2,\infty \right )$

$\left ( -\infty ,-2 \right )\cup \left ( -2,\infty \right )$

$\left ( -\infty ,\infty \right )$

$\left ( -\infty ,2 \right )\cup \left ( 2,\infty \right )$

$\left ( 2 \right )$

Correct answer:

$\left ( -\infty ,2 \right )\cup \left ( 2,\infty \right )$

Explanation:

The domain is the set of x-values that make the function defined.

This function is defined everywhere except at x = 2 , since division by zero is undefined.

Report an Error

View Algebra Tutors

Fatimah
Certified Tutor

Yarmuke University, Bachelor of Science, Mathematics.

View Algebra Tutors

Angela
Certified Tutor

Saint Josephs College, Bachelor in Arts, Mathematics.

View Algebra Tutors

Joseph
Certified Tutor

Bentley College, Bachelor of Science, Marketing. Bentley College, Master of Science, Organizational Leadership.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in Dallas Fort Worth, Physics Tutors in Dallas Fort Worth, GMAT Tutors in Phoenix, LSAT Tutors in Chicago, GRE Tutors in Seattle, Biology Tutors in Seattle, English Tutors in Denver, Computer Science Tutors in Chicago, SSAT Tutors in Chicago, ACT Tutors in Atlanta

Popular Courses & Classes

ISEE Courses & Classes in Denver, MCAT Courses & Classes in Seattle, LSAT Courses & Classes in San Diego, SSAT Courses & Classes in Atlanta, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in San Diego, LSAT Courses & Classes in Boston, LSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Atlanta, ACT Courses & Classes in San Diego

Popular Test Prep

MCAT Test Prep in New York City, SAT Test Prep in San Diego, ISEE Test Prep in Atlanta, GRE Test Prep in Seattle, GMAT Test Prep in New York City, ISEE Test Prep in Denver, SAT Test Prep in Miami, GRE Test Prep in Dallas Fort Worth, GRE Test Prep in Denver, ACT Test Prep in San Diego

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 1 : Algebraic Functions

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Functions

Example Question #241 : Grade 8

Example Question #1 : How To Find The Domain Of A Function

Example Question #2 : How To Find The Domain Of A Function

Example Question #3 : How To Find The Domain Of A Function

Example Question #1 : How To Find The Domain Of A Function

Example Question #2 : How To Find The Domain Of A Function

Example Question #3 : How To Find The Domain Of A Function

Example Question #1 : Domain And Range

Example Question #4 : How To Find The Domain Of A Function

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: